There are 3 main gameplay modes currently available in Synergy (since Beta 2):
Coop - Cooperative play is our main focus here, as our name clearly suggests. Play as a Team with friends and complete map objectives, or play through the Half-Life 2 campaign.
It's important to keep your team alive, because as the player count increases, your weapon damage will weaken and your enemies will become stronger.
Teamplay - this is a team-based player and NPCs vs. player and NPCs mode, where Combine and Rebels go head-to-head in combat completing team map objectives.
Deathmatch - standard, but classical Deathmatch. With the addition of the new weapons, even Deathmatch should make for an interesting game.
If you enable the life system, you can turn Deathmatch games into Last Man Standing and turn Teamplay games into Last Team Standing. For more information, read the section on the life system.
Be aware that gameplay modes are defined in the actual levels (However it is possible to convert maps to other modes, as long as you've got expirience with Valve Hammer Editor).
Levels with the prefix of "co_" or "syn_" indicate the level has been created for cooperative play and "te_" or "tm_" indicate a Teamplay level and "dm_" indicates a Deathmatch level.