The distinction is in how armored works:
All loss of life from attacks and destruction spells is reduced by one half, rounded down.
So, armored does not work at all against alterations, thus the creature can still be poisoned for example. In your example, since Gaze of Horror is an alteration, it ignores armored ability and works. Lava Blast is a destruction spell so it deals 3/2=1.5 rounded down to 1 damage.
It gets a bit harder to know what will happen when the loss of life comes from an ability, where it can be unclear if it is a destruction or alteration under the covers.