If one assumes that a minor planet is something that has a minor planet number, minor planets would indeed be a superset of asteroids, including KBOs (and some other stuff). The
IAU suggests that the term be replaced with the egregiously unwieldy "small solar system body" - if this is supposed to mean that the terms are equivalent, it would imply that comets are minor planets while Ceres isn't one!
We do seem to have accumulated a surfeit of poorly defined terms of solar system nomenclature. I vote we adopt the classification suggested by, IIRC, Clarke, in which solar system bodies are divided into the Sun, Jupiter, and dust.