Monero is switching to Cryptonight variant 4 (CNv4) in March 2019. CNv4 is based on Cryptonight-R, with some modifications. What are these modifications ?
What are the differences between Cryptonight-R and Cryptonight v4?
They are the one and the same thing [src], just different naming.
Cryptonight variant 4 aka CryptonightR
More accurately though, CryptonightR is proof-of-concept code and Cryptonight-v4 is Monero's implementation of it [src].
This is proof of concept repository and a proposal for the next Monero PoW. It introduces random integer math into CryptonightV2 main loop.
...with some modifications. What are these modifications ?
Just some final tweaks from vtnerd [src]. These are not fundamental changes, rather last minute "tweaks".
These last minute tweaks ensure the original developer of the implementation hasn't also secretly developed an ASIC capable of working with the implementation, and also any other ASIC manufacturers that might have been developing an ASIC whilst the code was available before being PRed to Monero.
Of the tweaks themselves, the addition of an extra register and more memory access routines seem to be the significant tweaks.