What's the difference between the different guitar model designs like telecaster, stratocaster, les paul and so on? Do they sound differently too or just look different in design? If they do sound different, what are their differences?
different sounds due to pickups mainly but different wood gives a different tone, also les pauls are generally heavier (as in weight) than telecasters so it's all personal preference.
Belief is a beautiful armour but makes for the heaviest sword.
They all sound different. Every guitar sounds different so there are far too many to simply list them.

mainly though, for the models you listed

Telecaster - very twangy sound, great for country styles of music

Stratocaster - great for blues and rock and good for just about any other style of music except for metalz. (most people that I know have started with a strat because they are very versatile and comfortable guitars to play

Les Paul - Very deep and rich tone, with the use of the 2 tone knobs you can get quite a few sounds out of them, they are very heavy compared to other guitars, and there's a model that will fit the bill for every style of music.