People do use this casual expression. Someone might say, "he is BEING annoying" when a young child does something to irritate you. Perhaps the child is running around the room so, at that particular moment, he is being very annoying. It would be better to say, "he is annoying me at the moment".

I think the first sentence is what he is at this particular time. The second sentence is what he is at all time/mostly. I might be wrong, but that is how I see it:-)

English Grammar in Use 4th edition by Raymond Murphy is excellent. The paper copy is reasonably priced and there is a PDF on the net. Unit 4E He is selfish (general behaviour) He is being selfish (temporary behaviour)