No, whether it is prostitution or not does.
So if I pay a woman for sex with me it’s prostitution but if I pay her for sex with another guy it’s not prostitution?
Here’s a novel legal defense concept - Bill and Bob want to hire hookers, but don’t want to break any laws - so Bill hires a hooker to service Bob and Bob hires a hooker to service Bill, and they both film it - this somehow converts illegal prostitution into legal porn?