The Designated Marksman, or DM, is not a sniper. They may use a sniper rifle, or rifle similar to what a sniper would use, but they are not a sniper. The DM has a very specific role that they fill within a squad, which is to take accurate shots(sometimes from a long distance) while sticking with the squad. This is the major difference between a DM and a sniper, the DM will almost always stay within the squad, while the sniper usually works in a smaller two man team.
If you the squad leader or fire team leader needs somebody dead, they will usually ask the DM to make it so while the rest of the squad gives them support and cover fire. The DM almost never acts alone though, they need to support their squad as well.
The DM usually uses a semi-auto long range rifle, such as a m-14, or SR-25, or even a M16. Usually they have a 4x scope to spot and take shots with. Although these guns all go full auto, they should almost never have to go full auto unless under duress. Most DMs prefer their guns to be shooting in the 400-550 range, to give them more range over full auto aegs. But this means they need to use engagement limits such as 50 feet or some other agreed upon distance. Under that range they should draw a sidearm, preferably a pistol so it takes up less space.
The key to being a good DM is taking accurate shots and working with your squad to get people in range and in the open for you to kill. DM is a more glamorous role than the sniper, as they get more shots, but will probably use similar gear to the rest of the squad. Basically they are a slightly longer ranged rifleman with a specific role beyond taking shots.