“What is the difference between marriage counseling and couples therapy?”

Not much, semantics a little.

Simple answer – nothing except the legality of marriage! Any "couple" (planning to marry, married, planning to divorce, divorced [to discuss children, for ex.], partnered, gay, etc.) can go to therapy to work on their relationship. Just another word for the same thing. So, whatever your relationship status is, you can go! Likewise, "counseling" and "therapy" are usually used interchangeably, although some might think counseling has more "advice" giving than therapy. You can ask the person you contact what their orientation is, and they ought to be able to summarize it in a few sentences (or, nowadays, you may find the explanation on their website.)

Peace, and good luck,

Dr. Marian K. Shapiro

Hello Madam, 

Marriage counseling means therapy/counseling for the couple that is legally married. Couples counseling means counseling for a couple that may or may not be living together. Hope this clarifies. 
Take care and remain safe. 

Dr. Lata Sonpal

There's not much difference. If the couple isn't married or about to get married, we don't call it marriage counseling. If the focus is on information, suggestions, or education, then we don't usually call it therapy.

Check out this link..
https://www.northbrooklynmft.com/marriage-counseling-vs-couples-therapy-whats-the-difference/#:~:text=Marriage%20counseling%20tends%20to%20deal,causes%20unhealthy%20patterns%20of%20relating.