Skills get a cast multiplier. When the skill is an instant cast, its damage is multiplied by 1.
If the skill has a cast time, its damage is multiplied by cast time.
So when multiplied by cast time, casted skills do more damage than instant casts.
So if Fireball does 1000 damage, and Flame does 800 damage.
The fireball's 1000 damage stays as 1000, while the Flame's damage will increase by 3 times (since it has 3 second cast time), and come out as 2400 damage.
The cast time multiplier is not affected by casting pots/buffs. Flame will always have a cast multiplier of 3, even if you get it down to .5 second cast time.