Is there a difference between draining, absorbing, and nullifying elemental damage in Final Fantasy 7?

In the original Final Fantasy 7, different equipment uses different terminology when describing protection against certain elemental attacks.

Aurora Armlet says “drains cold attacks”.

Ice Ring says “nullifies cold attacks”.

I see several sources that list some of these effects as “absorbs” cold attacks, but I can’t be sure it’s ever actually used in the game. Are these just translation quirks where it is inconsistent in what word to use? Or is there some different meaning in terms of game mechanics?

Based on descriptions of how elemental materia works when put on your armor, I would expect “absorbs” to be used if that element actually heals you, and “nullifies” to be used if that element just does 0 damage to you instead. But I’m unsure if any armor or accessory works this way, or if you can only get healed through the elemental materia.

Can't say what difference there is (if any) between "Drain" and "Absorb" since they can both be used to mean the same thing

"Absorb" and "Nullify" there is. Absorb will, as you suspected, heal you if that element is used against you while Nullify will zero out the damage of that element. I have personal experience with the Aurora Armlet aborning Ice as I use it along with the Fire Armlet (which absorbs Fire) against Schizo and later in the game I use the Tetra Elemental to Absorb Fire/Ice/Lightning/Earth

For something like the Poison Ring which the description is

Protects against Poison status. Absorbs Poison elemental damage.

it stops you getting the Poison Status while absorbing the damage of Poison attacks, combine the effects of a Mastered Elemental Materia paired with Poison on your Armor (which Absorbs Poison Damage) and a Mastered Added Effect Materia paired with Poison on your Armor (which prevents Poison Status but not stop the damage from the attack).

A quirk with Poison is that if you're afflicted with the status effect you take Poison Damage, so having a Mastered Elemental Materia paired with Poison on your Armor can lead you to getting a secondary means of getting Regen. No other status effect works like this