What the stats do, based on my experience with them and what’s covered in game. As a disclaimer, I’m writing this before a wiki on this is out, so what I say here is what the stats do based on my experience with them, and may or may not be 100% accurate.
Basic Stats
Capacity: How many bullets the gun can hold. Shown to the bottom-left of every weapon portrait.
RPM: How fast the gun is capable of shooting, measured in Rounds-Per-Minute. The bigger the number, the faster the gun can shoot. Generally more important in automatic guns, since semi-auto guns shoot however fast you press the button.
Accuracy: A measure in degrees how inaccurate your weapon is. The lower the number, the more accurate it is.
Penetration: How effected by armor a weapon is. How affected your shots are changes depending on the armor you’re shooting, but generally the higher the penetrative stat is the less effected your shots are by armor. With a high enough penetration stat, you can bypass armor to a degree entirely.
Noise: How much noise the weapon adds when you’re moving around. The lower, the quieter.
Volume: How far away your gun can be heard when fired in an open space, measured in meters. The lower the number, the closer someone can be without noticing the gunshot.
Mobility: How negatively a weapon effects your mobility. The lower, the less a weapon slows you down while moving.
Caliber: What bullet type a gun uses.
Advanced Stats
Shot Deviation: How off your shot can be. The lower the angle is, the narrower area a shot could travel away from where you’re aiming. (For example, 0 deviation means your shots will always go exactly where aimed)
Accuracy Recovery: How quickly your accuracy recovers when not shooting. Measured in multipliers, the bigger the multiplier the faster your accuracy returns to normal.
Aim Zoom Range: How much farther you can see when the aim button is pressed (the same button used to shoot out lights and such). Usually not applicable unless the weapon is equipped with some form of scope (like a sniper rifle).
Pellet Group Spread: Only applies to shotguns, a measure of how tight the scatter of the pellets are in degrees. The larger the degree, the wider the scatter and vice versa.
Spread Per-Shot: How much more inaccurate your gun gets when firing shots off quickly, most noticeably in automatic weapons. The bigger the number, greater your shots will deviate from wherever you’re aimed at.
Controlability: How easy your weapon is to control, such as how quickly your gun reaches maximum inaccuracy. Not sure how true this is but weapons with lower controlability seem to get more inaccurate far faster.
Max Additive Spread: The most inaccurate your gun can shoot, measured in degrees. The bigger the number the greater overall area your shots could deviate from where you’re aiming.
Turning Related Stats: Any time you quickly aim from one direction to the other, these stats are how negatively that effects your aim. Turn instability means your shots are more likely to deviate from wherever you’re actually aiming, and max turn spread is the range in which you’re shot is likely to go instead of where you’re aiming.
Mobile Accuracy: A percentage of how accurate your gun is while moving. The higher the percentage the closer your gun is to shooting no less accurately than when standing still.
Focus Accuracy and Focus Speed: Not sure what these do. I think they effect the respective fields while focused (any time slow-mo is happening).