Completely depends on the course. A scratch golfer at the club I play at goes to other courses and is closer to a 5 handicap. A scratch golfer at Augusta is probably pretty darn good.
With that said, there are hundreds of scratch golfers. I would equate it to a A+ to semi-pro. Pro is a whole nother level that 99% of the Semi-Pros will never get to.
Case in point... Probably the best golfer out of Ottawa is a fellow named Brad Fritsch. He has tried to get onto the PGA tour via Q-School and also playing Monday Qualifiers. In our Region, he would be a +4 handicap or better. He is simply a terrific player. He still can't crack the PGA Tour. He also has had limited success on the Canadian Tour or the Nationwide Tour.
Another quick example. Eagle Creek in Ottawa held a tournament for the Canadian Tour. The winning score was around -23 for four rounds. A scratch golfer shooting par wouldn't even of made the weekend. Now, compare these 'pros'.. not a single one of the pro's in the tournament ever played on the PGA Tour.
There is a whole other level out there.