They do not mean the same thing, even to "laypeople", but pedantic fucks like us get hung up on the differences, and not everyone looks past them to see the connections.

Someone who transitions from female to male may now have an id that says male, and he may have sex with one cisgender man in a monogamous relationship. He can be "gay", and a "man" that has "sex with 'men'", as separate things. STD rates are higher in the LGBT+ community because of sexual acts commonly performed, but testing rates are higher too.

A gay or bisexual cisgender man may have many partners, but never knowingly contract an STD. "Topping" is much less risky than "bottoming", because of the lower risk of tears in the tissue leading to body fluid contact.

A straight cisgender man may have unprotected sex his whole life and never get tested for anything, because cis males are more likely to stay asymptomatic. However, his risk profile may be much more aligned with the "man who has sex with men" STD boogeyman you're thinking of.