Assault Rifles are weapons with medium-high ammo capacity and the ability to place a lot of rounds downrange quickly. While they don't boast the ammo limit of Light Machine Guns, they trade it for much higher accuracy.
DMRs, or Designated Marksman Rifles are weapons between the Assault Rifles and Sniper Rifles categories. Broadly speaking, they've got just short of the range of a sniper rifle, and just slightly higher damage than an assault rifle, albeit with a slightly lower magazine size.
Sub-machine Guns are great close-range weapons that have the accuracy of most Pistols but get the magazine size and fire rate of one of the Assault Rifles.
Sniper Rifles are the ultimate weapons when it comes to range and power. In general, these rifles suffer from low magazine sizes and a cripplingly low rate of fire but are redeemed by their high damage and extreme range capabilities.
Light Machine Guns are essentially weapons that boast a higher rate of fire over Assault Rifles and a slight increase in bullet damage, but with a much higher drop off in terms of range and ammo carrying capacity.
Shotguns are weapons designed to fire shell cartridges that are different from normal bullet cartridges. Shells are usually loaded with a kind of pellets that can vary in size depending on the desired application. Because of the spread of the pellets, the shotgun is less useful over larger distances, as the traveling projectiles tend to travel away from the center of the predicted bullet path eventually covering the area much like a cone shape.
The crossbow is short to medium-ranged weapon. It does very high damage, with a shot to the torso capable of killing an unarmored enemy in one shot and headshots being instant kills. It is also completely silent, allowing for stealthy kills.
Pistols are great secondary weapons, but they can also function as primaries.