A 'modelling amp' has built-in effects that attempt to shape the sound in ways that imitate some popular classic amplifiers. Some of the newer ones ae pretty good at it.

A combo amp is an 'all-in-one' unit that has the amplifier and the speaker(s) in the same cabinet.

An amplifier 'head' is a box that has only the amplifier in it. It usually sits on top of a 'stack' of separate speaker cabinets, like the head on top of a snowman.