Control is the issue.
An A player can control a B player. The B player can run out, do a lot of good things but he can not control the match. He still depends on his opponent to give him another turn at the table.
An A player can control a match with a B player. He does this with many tools. Safety play, the break, kicking ability, pattern play, knowledge, etc etc. An A player maximizes his opportunities and creates new ones by putting the B player in positions he can't recover from.
Although everyone makes mistakes, A players make way less. And, most opportunities a B player gets from an A player are the shot after the break. An A player gets way more opportunities given to him by the B player.
A general rule of thumb is a B player can run out when given an opportunity. An A player can do that but can also create opportunities. B players do not create opportunities very well.