In Reaper, you have both Groups and Buses.
Well, no. (?)
In Reaper you have tracks.
Those tracks can be Folders which hold other tracks and can (usually do) also work as a group bus might. I think this is what you're calling a Group, but it's really just a track, and if somebody goes to search the user guide or the actions list for the word "group", this is not what they'll find.
Likewise, there's not really anything called a Bus in Reaper. Well, that MIDI bus thing, but I think that's poorly named. What you're calling a bus is just another track that you've got receiving audio from other tracks. There is nothing different about it just because you call it a bus, and you don't have to tell Reaper to create it as a bus. It's just a track like any other.
It is, in fact, completely possible to have a track with its own audio item set up as a folder ("group") with the audio from its children mixing into it and a bunch of receives from other tracks ("bus") mixing in there too. Then you could put some effects on that one track and they would process the whole mess. Don't know why you'd want to, but you could.
This might sound nitpicky, but I'm mentioning it for a couple of Reasons:
1) This is significantly different from most other DAWs out there. In fact, it's one of the selling points of Reaper. Last time I used Sonar or Cubase, if I wanted a bus that I could route other tracks to, I had to tell it to make a bus, which was different from a track in a number of ways. They both have folder systems, but IIRC correctly, they are just for organization and display and have nothing to do with audio routing or mixing.
B) This is the noob section, and I just know somebody's gonna open up Realer and start looking around for this Group you've mentioned, and they're not going to find it.