what means "rough around the edges"?

[pipelette]

the dictionary says: "If someone is rough around the edges, they haven't mastered something, though they show promise."

But I have heart this expression in other contexts:

1. if s.o. does not feel well, a bit frayed maybe, for example because of a hang over

2. if s.o. is not very sophisticated, distinguished, but unpolished and without manners

Which is the right meaning? And/Or are there difficulties in AE and BE?

[Tdol]

In BrE, it could mean either depending on the context.

[BobK]

A related idiom is 'a rough diamond' - s.o. of great value but not a master of diplomacy!

b