there are three types:
solid state,
hybrid,
and valve (tube)
very very very briefly,
solid state amps are what most ppl use at home for practice, decent cleans, most of them have sterile and weak drives. example: marshall MG series
hybrids are more or less the same as a solid state, has one preamp tube in the circuit. a marketing gimmick as the preamp tube hardly makes a diff. example: the 2 amps dime gave as an example.
tube amps. the real shit. most of the time too loud and costly for home use. but tube amps sound the best most of the time. pristine cleans, harmonically rich and responsive overdrive. example: vox ac30, marshall JCM800
to go more into detail, please google it.