I'm new to mounting rails on AR-15s and need to ask some rookie questions.
1.  What is the difference between a Weaver rail and a Picatinny rail?
2.  I just bought a RRA R4. What kind of rail does it have on the upper and on the tactical carry handle?
3.  Can I use a Weaver style scope ring on a Picatinny rail?
4.  Can I use a Picatinny style scope ring on a Weaver rail?

Sorry for the rookie questions, any help from the veteran shooters out there would be greatly appreciated.  Thank you in advance

Yes, there is a difference between Picatinny and Weaver rails. I cannot recall exactly what the difference is, but believe that it has to do with slot spacing or depth. Your RRA will have a Picatinny rail. As for interchanging rings, I do not know. If you are going to mount a regular rifle scope (not a red dot), I'd recommend the ArmaLite one-piece mount or a set of ARMS #22 throw lever rings.

Weaver rails have slightly narrower spacing between rails, rings made for Weaver and Pic rails are not interchangeable.  If your RRA came with the "tactical carry handle", sell it.  If not, don't buy it, there are better ways to mount an Aimpoint for which it was made.