Zone mark is to mark a space on the field. Covering mark (if you mean man to man) is to mark a player on the field.
It's not beneficial if you choose one strategy before the game and keep it as it is. Your defense will be much more efficient if you switch types during a game.
Man 2 Man: Whether it's passing to the foot, or sending the ball through an empty space, "man" is bound to be used sooner or later to get the ball in the net. Firmly keeping close to "man" and not letting him posses the ball, or if he did gain possession, not letting him move forward freely and blocking his way is the basic explanation.
A simple position change tactic executed by the marked man during the game is enough to weaken your defense line with the least effort. In that case have your man cover a zone instead. Any “man” entering your designated zone will be marked by your player. Compared to man2man this eliminates unnecessary running around the field and raises your defense efficiency.