Max Magicka and Spell damage are Magical offensive stats, while Max Stamina and Weapon damage are Martial offensive stats.

It's a combination of them both that gives you an "effective spell/weapon" damage. Proc sets that do damage scale off the weapon/spell damage side while proc sets that heal scale off the max stamina/magicka side.

Also light and heavy attacks now scale off the highest of the two. If your magical offensive stats are higher than your martial ones they'll scale off your Spell Damage and Max Magicka. Vice versa if your Martial damage is higher than your Magical damage, and this is true regardless of whatever weapon you hold in your hand.

One last thing I'll add is that crit is based off whatever resource is used while casting, and penetration is based on damage type done. Stamina cost abilities are martial scaling, while Magicka cost abilities are magical scaling so if they heal they'll scale off these offensive stats unless stated otherwise.
Health cost and Ultimate cost abilities depend upon the damage done and any rules listed in the ability. Ultimate damage/healing scales with the highest of your offensive stats like light/heavy attacks but their crit and penetration is based on damage done.

Fire, Ice, Lightning, and Magic damage are effected by Magical offensive stats, Spell Penetration, and Spell Critical.
Poison, Disease, Bleed, and Physical damage are effected by Martial Offensive stats, Physical Penetration, and Weapon Critical.

Sorry for the million edits lol. As I hit enter more stuff kept coming back to me in regards to the rules of how this stuff works. I found in the grey area that is health cost abilities typically they have their scaling rules typed out. If not they follow the damage type scaling everything else does.