This blows my mind. Has Bungie written up anything explaining all the stat categories?
I don't think so. You can mouseover stats to get more details though. Attack and Defence are the two weird ones. I believe they are essentially simple modifiers/multipliers to damage given and taken respectively. They are turned off in standard crucible modes.
The descriptions are all below. Some are a bit confusing to be honest. Attack in particular.
Rate of Fire: "The number of shots per minute this weapon can fire"
Impact: "The damage inflicted by each round"
Range: "Increases the effective range of this weapon"
Stability: "Decreases weapon recoil when fired continuously"
Reload: "Decreases the time it takes to reload this weapon"
Magazine: "The number of shots which can be fired before reloading"
Blast Radius: "Increases the explosion radius of this weapon"
Velocity: "Increases the speed of projectiles fired by this weapon"
Charge Rate: "Rate at which the weapon charges"
Blast radius & velocity are on rocket launchers, and charge rate is on fusion rifles
ATTACK: Higher Attack allows your weapons to damage higher-level opponents
DEFENCE: Reduces incoming damage from your enemies
Light increases your level, increasing the damage your abilities deal against higher-level enemies
Intellect reduces the cooldown time of [Current Super], allowing you to use it more often
Discipline decreases the cooldown time of your grenades...
Strength decreases the cooldown time of your [Special Melee], allowing you to use it more often
Armor increases the amount of damage you can take before dying
Recovery increases the speed at which you regain lost health
Agility increases your movement speed and maximum jump height