I am not a lawyer but would guess that if you offer or pay for sex for money than it would be illegal whatever you call it.

It's when any kind of sexuality gets involved that LE can make a move.

What exactly constitutes that does vary from state to state (Currently in RI, for example, anything that takes place behind closed doors goes, but they may not last long.)  Some states use vague language involving morals and such.

Your best bet is to never discuss sex or money openly and never to see anyone who does likewise.  Warn potential clients on your website as to your policy and stick to it.

If LE tries to target you and finds it hard to make a case, they'll most likely skip over you and look for easier prey.

(still not a lawyer)

It is legal to pay for time and companionship, unless that is a euphemism for sex.  Saying the words, "Time and companionship" won't buy a free pass when the ad shows a topless girl, you get there, exchange $300, and take off your clothes.  

It is like anything else in law. It doesn't matter what you call it.  They will look at the whole picture and let the jury decide.