There is a difference between pressing the play (that is, the area where the ball is) and marking (the area where the other players have positioned themselves to receive a potential pass coming from the other area).
Pressing may be considered as active while marking may be considered as passive.
press: go and put pressure on the player that has the ball or on the player that has positioned himself to receive the ball
mark: focus on a player; put yourself in a favourable defensive position with respect to the player so that you may make an interception in the case where he might receive a pass or prevent him from progressing in the case where he was able to receive the ball.
Both can be said to result to the same things, that is intercept a pass or prevent a player from receiving the ball, but they do it in different ways. But, pressing provides something else: forcing the player that has the ball to act quickly or else concede possession. That is, it reduces the time a player has on the ball. This is why I say that pressing may be said to be active while marking may be said to be passive.
Marking is highly involved when defending set-pieces and crosses.
Pressing may be more involved in 'open' play situations.
A good combination of marking and pressing is what makes a team good defensively and also prevent the other team from keeping possession. One or more players press the players in the zone of play or close to the zone of player, while the others mark the rest.