Difference between Facultative Aerobes and Facultative anaerobes

My Prof started off talking about Aerobes, there being obligate aerobes and those that can metabolise compounds such as $ce{NO3-}$, $ce{SO4^{2-}}$.

Then he began talking about anaerobes and those that can process $ce{O2}$, calling them facultative anaerobes.

Are they not the same thing?

Edit:

Prof has responded that yes, they are the same thing, though he didn’t say why. My guess is that anaerobes simply refer to organisms that can use things like $ce{NO3-}$, $ce{SO4^{2-}}$ to respirate, aerobes simply refer to organisms that can use $ce{O2}$ to respirate, and facultative refers to how they can tolerate the condition opposite to the one they can use.

ie facultative anaerobe = anaerobe, but can tolerate oxygen
(facultative aerobe = aerobe, but can tolerate the lack of oxygen)

Anyone can verify if this is correct?