In my experience it’s both 😁

I grew up an Orthodox Jew (I’m not as an adult). The way I learned it was that existing as a gay person, as in, that’s simply who you are, isn’t problematic. The issue is the act of gay sex itself, which is what the verse in the Torah refers to.

That is to say, your understanding is correct.

Disclaimer: I don’t care about it myself. Just explaining it how I was taught in Orthodox schools.