Awareness is being able to complete the play or ur assignment better. Being aware of whats goin on. Being aware of situation. Making smart decisions that wont hurt.
Play recongnition is recongnizing the play before the ball is snapped. in the NFL defenses and players notice certain packages and formations. And by that they can recongnize the play. Thats where "play recognition" comes. Recognizing the play before it unfolds.
Pursuit- Lest say there is a toss towards the right side of the offense. And a players is a ROLB. (they are running the ball away from him) The greater the pursuit, the better he is on making the hit/tackle. Pursuit, catching/chasing/running down the person with the ball. Like u said above how aggresive he is getting the ball carrier.
Did that help?