I'll restrict my observations to men's pool here.
There is no such thing as "turning pro" in America. Once upon a time, when there were national tours for which you had to qualify just to participate, those who, on merit, became permanent members probably had a right to call themselves pros. Today, only those who have sufficient earnings from competing to pay all their bills in life are worthy of being called pros. In America, that's probably about ten people, and I'm not sure players who carry a Fargo of under about 760 have a right to call themselves pros.
There are players who play at a speed approaching the speed of the true professionals, and I like to call them "top level amateurs", corresponding, in my mind to a Fargo of 725-760.
There is also the intent to turn pro, committing oneself to sufficient participation in competitive events with the goal of one day being able to pay all the bills from pool earnings. Players in this category might be called "potential pros" or "aspiring pros" but they are not pros.
To sum, in America, nobody is quite sure what a pro player is. For most of us, it's no more than a perceived level of excellence. As I've noted, for me, that level is Fargo 760 or better, but another measure might be "any player that frequently posts top ten finishes in major events or top regional events."
Of course, there are also "teaching pros" who make their primary living from pool instruction, and they, too, are worthy of being called pros. Certainly, the likes of Jerry Briesath, Mark Wilson, Randy Goettlicher, and Scott Lee are all pros, as are other comparable instructors.