Do moustache, goatee and beard have corresponding words respectively?

moustache: it is called moustache (beard on the lips) in general, and moustache also has many shapes, such as fu manchu (moustache of Fu Manchu style), Handlebar (moustache of bicycle handlebar style), copstash (moustache of police style)

goatee

Beard: it is also called full beard.