It's very complicated to explain. I'm exhausted just thinking about trying to answer you.
The short answer is: They used to be totally different prior to the 1930s, then they were mostly the same with different trim up to the 90s, then BMW bought Rolls and VW bought Bentley (1998 I believe) and for a while they were being built in the same factory (I think they still are) and BMW was supplying VW with V-8 engines for the Arnage; as of now, VW is probably going to base the next Bentley on an Audi A8 chassis.
So I guess my answer is that they were similar from 1998 but they are diverging. I can say that they are definitely competitors and I can say that there is no connection anymore with Rolls Royce Aviation or the old Bentley people.
These are fundamentally German cars built in England.