Not to make anything more complicated, but should also mention PMHNPs (psychiatric mental health nurse practitioners). They do therapy, and can also prescribe. Depending on where you live, they have various levels of "prescriptive authority". In some states, they have full prescriptive authority, in other states they have various arrangements with MDs for prescribing procedure.

Since it's kind of unusual for psychiatrists to do therapy anymore, and mostly (or all?) the other therapy options can't prescribe, thought it'd be worth remembering this "two-fer" (that doesn't look like it's spelled right-- anyway, I mean two in one) option.