We know that "to be" verb is not normally used in any continuous tenses except when it means "to behave"
To be :
6 [linking verb] to behave in a particular way
He was just being rude.
After "to be", we can have an adjective. However, after "behave", we have to use an adverb as in "The doctor behaved very unprofessionally".
My question is
Are "She is being rude/unprofessional..." and "She is behaving rudely/unprofessionally..." roughly the same?
Or is there any difference between them?