Oh, boy....this is gonna take a while !
The RS4 was never offered in any other form than Avant, unlike the S4.
The RS4 is basically the Escort Cosworth of the Audi world.
Audi sent the S4 off to cosworth to tune it and style it and they came up with the RS4.
Styling (flared arches, sills, etc)
Uprated brakes (needing 18" rims to go over them)
But most importantly the engine
Although the RS4 and S4 share the same engine, the internals are way different. Bigger turbos, larger inlet/outlet ports, manifold, etc etc.
The difference ? (apart from the obvious styling)
265BHP for the S4
380BHP for the RS4
To cut a long story short (since i've owned both)
The S4 is very torquey.....thanks to smaller turbos which spin up quicker, smaller ports etc etc but runs out of puff top end
RS4 is the other way round, bigger tubos, and ports, not as good torque as the S4 but top end is out of this world.
hope this helps ?