Traits make a difference.
A defender that has "Yes" for his pass rush moves can be a bigger force. A Big Hitter: Yes guy can cause a lot of fumbles (and probably knock balls loose from receivers just as they catch them?)
Plays the Ball: Aggressive will see guys attack any floaty ball or attack the ball more often. Conservative guys will tend to make the tackle, unless the ball is pretty much right at them or have other ratings that let them get a jump (high PRC and AWR, for example) - and then they "get in better position" instead of "attack the ball" (subtle difference in how the play resolves, imo).
Brace for all hits will make the ball carrier curl up into a fetal position when a big hitter/high POW guy comes around.
Clutch: Yes players sometimes (Often? Always?) get a "boost" when the game is close and in the final two minutes. Doesn't mean they'll be perfect, but they'll usually play harder. High motor impacts how far away the play can be from the player for them to continue to try to make a play/give pursuit.
And so on.
Some might be gained/lost on ratings/other factors, but they impact the player during the game and can change mid-game based on what happens to the player.