I would guess nonverbal communication is the back and forth we do, but not with words.
The nonverbal language would be (maybe!!!), our specific way of communicate without words.
Like for sure I have a nonverbal language but mostly people knowing me understands it. Other people seem to get it ALL wrong.
I think also a nonverbal language can be cultural. I have seen an Italian woman who spoke my language perfectly, but her gestures were still Italian. And Americans come across to us Scandinavians as.... um.. somewhat crazy, because the difference in nonverbal language. They seem out of control and overly emotional. They might not be, it is just that if a Scandinavian would act like that they would have to be a little nuts. So yeaaaaa, a lot of misunderstandings can happen! I've thought some foreign people were like stalkerish because of their nonverbals. The same goes the other way around, Americans mistake us for being rude and uncaring.