On average, a '3 pick-up' guitar is going to be a Fender Stratocaster style guitar with three single coil pick-ups. A 2 pick-up guitar is going to be more of a 'Gibson' type guitar (Les Paul etc).
Now this is not at all a hard and fast rule. Not at all. Gibson's sometimes have a single coil type of pick-up in them and Strats definitely can have humbuckers in them.
For a sound difference, check out this video. It's simple and doesn't explore all kinds of music but you can get an idea of the differences.
Both offer great sounds but it depends on what you are looking to play and even with musical styles, each can be applied in different ways.
So the difference is what really sings to you.
