Well....usually groups that have nothing to do with each other tend to just leave each other alone and pretend the other group isn't there. There are some rps that tend to have a few groups that tend to rp rivalry and all that. So I'm guessing it just depends on the situation of the rp?
Regarding roleplays -- allies and rivals are like friends and enemies.
An allie, usually offers the group IC (in character) supplies, training, etc for the group it is allied to.
A rival on the other hand, offers the roleplay and groups juicy drama and conflict. Something to keep members on their toes.
This is the general idea but I don't think I've seen many groups other than the Benevolent with the Malevolents back in the day keep this allie rival thing up to par. Hope this helped somewhat. c: