Hello MusicPebbles.
Well sure there a lot of types of electric guitars. Brand wise, configuration wise, there are many many variations.
First of all there are brands, Fender, Gibson, Ibanez, Epiphone, Taylor etc etc..
each has a quality of their own.
Basically breaking down your question of different types of electric guitars, there are solid body guitars which one big piece of solid wood with the neck attached to it, via bolt on or neck thru or set neck.
Then there are hollow body guitars, which have their insides taken out, it is sort of like a semi acoustic. Examples would have the ES-335 by Gibson.
Electric guitars are also classified into the shapes they are commonly known by.
There are, the strat types,(fender stratocaster, sx strat etc etc..) the single cut types, (gibson les pual, fender telecaster, PRS SE etc etc..) the super strat types, (Ibanez RGs etc etc..)
Each type has a personality and tone of its own.
The wood plays one of the most important factors into guitar tone. There would be basswood , mahogany, ash, alder, poplar just to name a few.
Guitars are also classified by their pickups they are armed with. Pickups are the electric guitars' microphone if you must know. There are single coils and humbuckers.
Single coils give you clear, crisp, twangy sound, they look like well a white singular bar, while the humbuckers give you dark, deep, warm, mellowish sounds, they look like a big rectangular block.
These are i think the main points for you to look out for the different electric guitar types.
So summarizing, i guess you gotta look out for what shape, type of wood, and pickups.
Visit
www.wikipedia.org for more information if what i typed here wasn't sufficient =]
Cheers.