There are two game modes in Shadowgun: Deadzone, namely Deathmatch and Zone Control
For more info, see: http://shadowgundeadzone.wikia.com/wiki/Deathmatch
Deathmatch is unlocked as soon as you begin playing Shadowgun: Deadzone. The main objective is to score as many points as possible, with the person with the highest number of points getting an extra reward for being first. Deathmatch maps are kept fairly open, so you need to be aware of your opponents as well as weak spots in your hiding place/sniping spot should you choose that method of playing. To sum up the objective, kill everyone in sight without losing your own life in the process. But if you do die, don't sweat it- a simple 5-second spawn screen stands between you and your rebirth.
For more info, see: http://shadowgundeadzone.wikia.com/wiki/Zone_Control
Zone control is unlocked at Rank 4. It differs from Deathmatch in one main way- winning it is a team effort. The main objective is to secure and defend as many of the five zones on the map as you can along with your team-mates. You are placed into one of two 'teams'- the blue 'Shadowguns' or the red 'Mutants'. Killing opponents and securing zones will cause the other team to lose points. Once they have 0 points left, your team wins. The other way to win is to have all five zones controlled by your team. If you die, a 10-second spawn screen awaits you.