Correct, Aren't you both saying the same thing? Doesn't empower, maximize change the spell level as well?
No.
They use spell slots that are higher but the spells are still the same spell level as written.
The "effects" have changed.
For instance an empowered fireball is still a 3rd level spell (wizard version).
It takes up a 5th level slot.
Its effects are increased by 1/2.
So assuming a 9th level wizard (minimum level to get a 5th level slot).
Casting at maximum caster level (you can always cast at lower levels but minimum of 3rd level in this case).
Normal effects are 9d6.
Empowered would be 1 1/2 x 9d6 and use a 5th level slot.
But the saving throw is still as if it was a 3rd level spell.
DC = 10 + spell level + Int bonus (for wizard)
Only heightened spells actually change the spell level (it even says so in the feat description)
"Unlike other metamagic feats, heighten spell actually increases the effective level of the spell that it modifies. All effects dependent on spell level (such as saving throw DCs and ability to penetrate a lesser globe of invulnerability) are calculated according to the heightened level. The heightened spell is as difficult to prepare and cast as a spell of its effective level."