Clutch playing has a ton to do with confidence - a ton rides on the mental side and a person's makeup. The ability to "free stroke" under the gun of a tournament or for the "chee$e" is what is important. If that back stoke arm tightens just a bit under pressure - your game changes and your confidence falls.
I've seen guys who can run 100+ balls several times a day and then can't get out of the 1st round of a tournament - not because of who they are playing, but because of the weight of a couple of bricks on their backs.
Mind set for money and tournaments are totally different also. For the cash it is up to you how far you will go, how much you will risk, how bad of a hurting you are willing to take. The tournament is structured (beginning, middle, end) - you are told who to play, when to play and basically how long you will place (per match). Some people thrive on structure and excel in tournaments - where others I've seen literally taking a $$$ beating at the table - down $1000's and keep going and seen them come back and win the cash in the end. No time limit, can go on for days with the same 2 going at it.
My experience from what I've seen is that, typically, the player that plays jam up for the $$$ can adapt and do well in tournaments, whereas the better tournament players, that don't really gamble, can have more problems crossing over to the unknown side of gambling. Of course there are exceptions and I'm talking playing for bigger $ amounts, not sets for $50 or $100.