There are tons of names for the same thing and if you look them up by the common name you get different pics and sometimes different care.
All the more reason to stick to scientific names. Obviously, knowing a generic name, isn't going to provide you the proper information, considering "There are tons of names, for the same thing, and if you look them up by the common name, you get different pics and sometimes different care."
Take, for instance, "cauliflower coral." While some may call Pocillopora a "cauliflower coral," "cauliflower coral," more commonly refers to a soft coral, in the Capnella family, or even a particular Leather coral, which have completely different requirements than a Pocillopora.
Sticking to scientific names, will usually get you the best advice, even if all you know is a genus.
In the case of Pocillopora, "Pocillopora" is a much more commonly used "generic" name, than any other word. You'll find it's almost always referred to, as "Pocillopora."