Genuine RS4 wheels - the ones of the twin turbo uber estate - are 18 x 8.5 and made of magnesium, and have an offset of ET20 to fill those wide arches and a stud pattern of 5x112.
RSTT's as fitted onto the supposed limited edition Audi TT's, then later made as standard equipment on S-line spec TT's, much to the delight of customers who paid a premium for the limited edition will fit straight onto your S3, as they share the same floorplan and hub arrangement. These are 18x8, ET33(I think?) and have a stud pattern of 5x100
The difference visually is the groove around the spokes on each alloy, the RS4 only goes halfway down the spoke, then blends in, where as the RSTT has the groove all the way round, making them look more dishy.
Replicas are just that, just a copy of the original wheels, but they offer both the RS4 and RSTT for multiple of fitments throughout the VAG range, with the main difference being the nasty centercaps you get with them, where as the Audi items get nice, properly finished centers.
Hope that helps!.