For regular people, I think it's mostly a matter of semantics. I call mine a counselor, but he's a licensed therapist with all sorts of alphabet soup after his name.
.
If you asked someone in the psych field for the official difference, they would probably tell you that anyone without a degree can be a counselor, but only someone who has achieved one of a certain set of degrees can be considered a therapist. So officially, it's about how much training they've had.
.
If you're looking to begin HRT or get letters of any sort, you're going to want to see someone who has a degree (therapist) of some sort to give their recommendation weight with whatever doctor you give the letter to. If you're just sorting out life issues, and such letters and recommendations aren't important...it doesn't matter who you go to as long as you feel you can work with them.