Since this is all speculative anyways...

I think cards relate more to tackling skill than aggression (you could review your carded players vs tackling instead). Or tackling and strength vs dribbling and strength of opposing player).

Aggression, I think, might relate to how well a player can close down on the ball, another player, or a passing lane. One of my better defenders has relatively low aggression, about 118. If he's marking someone, he can clear the ball or deflect shots. If he's not marking someone, it sometimes looks like he's picking daisies in the middle of the field. Can't be bothered....

I've wondered if arrows might affect aggression. If a player is more willing to close someone (high aggression) and stick their foot in for a tackle (bravery might be involved), then a low tackling skill might make him more foul prone. Coincidentally my fair tackling, low aggression player does well with an up arrow in many cases.