or electronic drum kits using pads you have to hit with a drum stick, just like when you'd be playing a real drum kit?
That one.

Essentially a drum computer with a real drum kit as sound creator (output), whereas the electronic drum kit uses a sort of drum kit as input.
For whatever reason, that's what I envisioned when I read the name "Drum trigger" and saw the picture of one. It wasn't until later that I thought "Hey wait; from the way people are talking about them, I think the "trigger" is more a sensor that detects when you hit a "real" drum head, and then produces an electronic output.

I'm still not sure, haven't had time to read about them.

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I'm like one of those idiot savants...well, except for the savant part.
"In order to increase awareness of the homeless, security have been given binoculars."