Generally, regardless of the legality of prostitution I suspect it would in most cases be treated as a civil matter and not a crime at all, like most disputes over payment for services. Where prostitution is legal, workers or their employer would be able to bring civil cases against clients who refused to pay if they could secure the relevant details. This is why most brothels in places where prostitution is legal require payment up front.
If prostitution is illegal, however, it may be possible to bring criminal charges for solicitation.
Obviously, using threats, force or other coercion (but not lying) to either obtain sexual services or avoid having to pay for them is very illegal, and the former is sexual assault.