[Question] Weapons! How do they work?

The easiest way to explain it is that Impact defines the base damage per bullet, and Attack Power defines how well the weapon will scale against higher level enemies. It's a little bit more complicated than that, but that's the base mechanic.

In Crucible, all players are considered to be the same level, so Attack Power is completely irrelevant. Only Impact matters.

Note that Sniper Rifles have something Funky with their listed Impact stat, so you can't compare a Sniper Rifle's Impact to any other weapon, only to other Sniper Rifles.

And as for PVE, does a weapon with higher impact, but lower Damage output work better on the mobs

I'm going to assume that by 'Damage Output' you mean 'Attack Power'. The short answer is that you should ALWAYS use the higher attack power weapon on mobs. All weapons within a given class are balanced to have the same DPS, so a higher impact weapon also has a lower rate of fire. This means that a lower Attack Power weapon will always do less damage than a higher one.

The long answer is that if you're comparing weapons of DIFFERENT classes, it can make a difference. Fatebringer is the best example, it's a Raid Legendary Hand Cannon from Vault of Glass (300 Attack Power), and it has the Firefly perk, which is AWESOME.

Now, normal Hand Cannons can't have Firefly, so if you're currently using Fatebringer, and you want to go to a 331 AP weapon that also has Firefly, you have to use a Scout Rifle.

Now, the difference in Impact between a high Impact Hand Cannon and a High Impact Scout Rifle is high enough that even with the lower Attack Power, the Hand Cannon will hit harder (although it will shoot slower). This is often ok because if the Hand Cannon will kill something in one bullet where the Scout Rifle requires two, it's worth it to fire a bit slower.

Regarding damage type, the only time it matters is for shielded enemies and burns. Against shield, using the right elemental type (i.e. matches the color) does 300% more damage. Trying to knock down a shield with the wrong damage type really slows you down.

Every enemy faction has two elemental shield types that can appear. Fallen and Hive can have Arc and Solar, Vex and Cabal can have Void and Solar. The enemy type you're fighting should determine which elemental damage types you have equipped.

/r/DestinyTheGame Thread