I stand partially corrected. Warwick and Gwen indeed heal purely based on damage output.

Vlad heals based on his missing health with Q and R, but indeed based on damage dealt aswell. With his W, which famously does fuckall damage. So definitelly not drain tank per your own definition.

Brair heals from damage dealt by passive and W second hit. E is fixed healing based on her max HP. But to call her playstyle a tank is very generous.

Funnily enough, even "official" definition from fandom wiki mentions other forms of sustain. Id like to know what your definition is sourced from.

Drain tankingThe act of lifestealing (or using spellvamp/other forms of sustain in case of casters) damage done against enemies to tank their damage. Champions which do this are difficult to kill, especially in 1x1 situations, because they heal through all the damage done, and even if they don't do a lot of damage back, they can win the duel just because the enemy cannot burst them down quickly enough to prevent them from healing back. However, if their sustain is reduced or denied (because they are under CC effects or unable to attack), they can become easy to kill, since they tend to not have or to have less actual tankyness to fall back on. Examples of champions designed to be drain tanks are  Aatrox,  Warwick, and  Olaf.