(not a professional teacher). That's a pretty good summary.
I can't really give you any time, but if you're quick I might be able to squeeze you in.
I really can't give you any time, you'll have to come back later.
"can't really" indicates a reluctance, perhaps a difficulty or an impediment to accomplishing the action being discussed, "really can't" means "absolutely not", "not at all", "in no way", etc. At least, that's the usage here in NZ.
Student or Learner