Wow Bor. That's, like, concise and stuff. Here's the Fannified version:
Every second of cast time on any spell gives it a damage multiplier, Wake. So, like, Flame has a cast time of three seconds- that gives it a cast time multiplier of three. Fireball is an instant cast, so it has no cast time multiplier. A priest's Rising Tide has a two second cast, so it has a cast time multiplier of two.
So, let's do some math just so you can see clearly why Flame hits so much harder than fireball. All numbers are made up, but they'll show the relationship:
Fireball: 50 damage, instant cast, does 50 damage.
Flame: 50 damage, 3 second cast, does 150 damage.
Rising Tide: 50 damage, 2 second cast, does 100 damage.
Now, imagine that you could get a spell like Flame to take .5 seconds to cast? Then you'd be able to do a lot more damage, because you'd still be getting the cast time modifier without having to take the time to cast the spell. That's why mages use a lot of cast time reducing buffs in a boss fight. That's where we get all our crazy burst dps. For about 30 seconds, any mage can get .5 to .7 second flames if they use buffs like guitar, Ancient Spirit Water, Arcane Potion and our skill Elemental Catalysis (which gets interesting at level 65).
Mage dps is pretty sad outside of our burst mode, but in burst, when we have all those buffs on, we can cast about 5 or 6 flames in three seconds, so we end up getting a lot of bang for our flame buck.
Cast time multipliers work on all spells that have a cast time- even Wardens have them, even Scouts. That's why Snipe hits so hard.