Is "restore" healing?

Absent any specific ruling/errata, when a card "restores" something to X HP, does that count as healing?

If it does, we found a hi-larious combo :-)  We were in the Court of Blood, and Unhallowed Halls was out, preventing all non-vampire healing.  The vampires spent the majority of the game attacking Greazer's Impeccable Pompadour, driving it further and further into the negative.  And every turn, Greazer looked at his totally non-perfect hair, and cried for 3 HP of damage, but unable to fix his hair.

Regain and restore are different terms.  Health can still be restored if Health can't be regained.

There is no such term as "healing" in Sentinels.

There is recovery as a term as well, but that has only applied to Regaining health so far.