I personally like the approach that I heard from Rav Zev Leff shlita.
He says that the difference is why you’re doing it.
A person could say: “I need parnasa. How should I make money? Instead of becoming a plumber or a lawyer etc., I’ll sit in kollel.”
This person is disgracing the Torah. He’s using it like a tool in order to support himself (like the mishnayos from avos that Rambam quotes).
The other person has a desire to serve Hashem and involve himself in avodas hakodesh- be it full time learning, kirub, teaching or any other tzarchei tzibbur.
But he says, “if I take a job to support myself, I won’t be able to dedicate myself fully and properly to avodas hashem! I have no choice but to take money for my avoda.”
This person is kodesh kedoshim and it’s a mitzvah to support him.
Rav Leff adds, how do you know which category you got in?
If you are in a situation where your needs are met and you are asked to serve Hashem. His example was a rav who gets an adequate salary from his kehilla, and is asked to give a drosha some where where they can’t afford to pay him.
If you wouldn’t go without getting paid, then you’re using the Torah as a tool and you’re mechalel shem shomayim.
If you would go anyway just to teach Torah, that’s assign that you’re kodesh kedoshim.