This is one I ought to know

We hear of the Theories of gravity, relativity and evolution and yet we hear of the Laws of Motion, Thermodynamics, cooling, Biogenesis

What is the difference between a law and a theory? They appear to be synonymous

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short answer: a theory is bigger.

A law is generally a simply-stated principle, like "the laws of physics in one initial frame of reference are precisely the same as in any other" but a theory is an entire model of part of the universe--e.g. special relativity takes the above principle, along with "the speed of light in a vacuum is measured to be the same regardless of velocity of the source or measurer" and from that is deduced the Lorentz equations. From these you could deduce other laws, or properties, such as time dilation, etc.

Actually I said "principle", but usually, a principle is something emergent, such as the laws of thermodynamics, presumably emergent from relativity and quantum mechanics--in chess, the laws are the usual rules of chess, the entire system of rules is the theory, and emergent principles are strategies (like--try to achieve control of the center of the board near the beginning of the game).

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No small part of the Wikipedia: Theory, is devoted to comparing and to contrasting science theory with science law (which has its own article, Wikipedia: Laws of science that briefly does its own contrasting):

Sounds like a matter for wordsmiths.

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A slice of apple will never be a pie, and a pie will never be an apple, but the overarching thing is to be given an apple pie (with a little ice cream on top).

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A law invokes respect. Legislated laws are to be obeyed, but scientific laws can not be disobeyed (within boundary conditions). This gives confidence to those that use them properly in designing bridges, for example. Better to build a bridge using laws than principles.

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These are all good answers. It should also perhaps be pointed out that in practice the difference between laws, principles, theories, and hypotheses are really not so cut-and-dried. It is very much an alive language, rife with contextual connotations, which in some cases allows these terms to be used almost interchangeably. So that's what causes the confusions about them. But when it behooves us to clarify the distinctions, the above answers provide a useful framework for making those distinctions. In some contexts, the distinctions can be quite important, whereas in others, they just don't matter very much. In particular, in actual science research, the distinctions are virtually nonexistent, in education, they are much more important, and in communicating science to the general public, they are paramount for avoiding misunderstanding.

The way I understand it, though like almost everything in life there is bound to be exceptions, a law is an observed principle. Such as the law of gravity that states when you drop any object with mass on an Earth massed and sized object, it will (discounting air resistance) attempt to accelerate to the center of the object at about 32 feet per second per second. If you have the same starting conditions, you will get the same results.. An hypothesis is an attempt at explaining the results. What IS gravity, what is it that makes things with mass accelerate to the center of an Earth sized and massed object at about 32 feet per second per second, what gives things mass PERIOD? A theory is an hypotheses that experiments have shown to be consistent with the way the world works as known at the time. Such as the theory of relativity as an explanation of gravity.
Over time observations are made that are inconsistent with the predictions of the theory, and so scientists start thinking of a new theory that a) explains everything the old one explains, b) explains the new observations and hopefully c) predicts new observations that scientists attempt to observe.
Please correct any errors I have made here please.

[edit]Thank you hhEb09'1 for the corrections.

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My favorite explanation is this: a law is an equation, and something that isn't an equation isn't a law.

I always thought it was the difference between what and why ...

what happens => law
why it happens => theory

so that there can be both laws and theories dealing with ... gravity, for instance ...

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I like both these, but I then to think “law” is an archaic, that doesn’t get assigned to new science (while most of the of the classical laws have been downgraded to mere guild lines)

per secondper second
Sure thing!

are you sure about that?

I think there might be a whole bunch of rock-doctors (geoscientists) who'd disagree with you -
the law of superposition, and the law of cross-cutting relationships spring immediately to mind ...

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It seems obvious why this might be a confusing discussion.

According to Webster

Law - (in regards to science or math) - a statement of an order or relation of phenomena that so far as is known is invariable under the given conditions

Theory (Entry 1 of 38)

1: the analysis of a set of facts in their relation to one another
2: abstract thought : speculation
3: the general or abstract principles of a body of fact, a science, or an art <music theory>
4 a: a belief, policy, or procedure proposed or followed as the basis of action <her method is based on the theory that all children want to learn>
b: an ideal or hypothetical set of facts, principles, or circumstances —often used in the phrase in theory<in theory, we have always advocated freedom for all>
5: a plausible or scientifically acceptable general principle or body of principles offered to explain phenomena <the wave theory of light>
6 a: a hypothesis assumed for the sake of argument or investigation
b: an unproved assumption : conjecture
c: a body of theorems presenting a concise systematic view of a subject <theory of equations>

I'm not going to post the next 37 definitions that involve the word "theory". I will note that even theories that have been abandoned, or are now considered untrue, are still called "the theory of " or something like "the steady state theory", which doesn't help at all.

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Yeah, it's just not cut-and-dried. Even the Webster definition of law isn't correct in any kind of reliable way, it is just an interesting distinction to draw. For example, we often talk about the "ideal gas law", even though it is well known its limitations and it does not conform to the above definition of a law. It is more like the "ideal gas model" or "ideal gas assumption", but we call it a law because it is a simple concise mathematical statement of a useful idealization. The same is true for Kepler's laws, for that matter-- there is actually "Newton's modification to Kepler's law", and even that isn't a law by the above definition, unless by "given conditions" they mean "the very ideallzation that defines the law". Which is pretty circular. Let's face it, words are fluid and contextual, and dictionaries do not save us from the fact that communication is challenging.

You might think that Science would require strict adherence to clear definitions of words, due to the importance of communicating findings to other scientist, with out errors or misunderstandings. Science builds on what has come before, and often it is critical that no errors occur, especially with the modern complexity of both systems and hardware, that are often incredibly complicated, with thousands of people working to complete a single device.

Yet at the most fundamental level, the very concepts, rules, laws, and principles that are used every day, seem to be confusing.

This can't possibly be the case in the real world.

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Yes, that's just why I often point to a difference between science and the real world.

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Logic is the grammar of truth.

Meaning and absolute certainty are incompatible, and profound meaning and absolute certainty are profoundly incompatible.

The only thing intelligence is capable of is recognizing itself.

I think, in general, science [both laws and theories] is more about whats and hows than whys.

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Yes, and one can see how true that is by considering the questions: What is science? How does one do science? Why does one do science?

I’m certainly in a minority in thinking "law" is an archaic term, but IMO it implies a false level of certainty that doesn’t really exist. I find that most modern scientists don’t like to suggest they are providing certianty. Laymen, however, often latch onto this false certainty and get lead away from how&why science really works.

Science is really about finding the best, most productive answers. Demanding absolute certainty about the natural world tends not to yield productive results and belongs to theologians and philosophers not scientists. I think the language should reflect this.

Exactly, that's it in a nutshell. And note this can be, and generally is, a moving target.

Once again, the conversation veers into a philosophical discussion. In the real world, such comments usually results in somebody older and wiser counseling you to use some common sense.

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Which really tends to kill a conversation.

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given that in science, why x happens is composed of what, when and how,
rather than some "search for purpose", I have no argument with that ...
though I question whether laws are truly concerned with the how ...

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Without wanting to sound too trite...

"Theories are subject to re-definition...while Laws are less gradually modified..."

Author...unkown

Well, in the real world, the definition of Laws is not an issue. It would be like arguing over what a plus sign (+) means in an equation.

2+2=4 Of course in Math it is very clear cut. But in Physics, laws are like equations, they are used to calculate and design. There is no doubt about their functionality.

Part of this is just like with math. The very definition of a law defines when it is true. Laws are also relatively easy to demonstrate, and are considered to never change.

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Except that most of the laws of classical physics are now considered approximations of a better answer. In a sense the are simply very accurate rules of thumb.