Ability damage is never described as such in-game, instead being listed as physical, magic or true damage. However, those typings can be attributed other archetypal damage types (e.g. basic attack damage can be physical and magical, too) and so knowing whether or not an effect deals ability damage can be hard to intuit.
The basic rule is: all damage-dealing abilities, excluding attack effects, deal ability damage.
Note that, however, the damage dealt by these abilities is not classified as ability damage, except in the case of Whiplash and the magic damage portion of Urchin Strike. Except in those cases, the damage dealt by these abilities will not benefit from Spell Vamp. It is possible—as with Non-Damaging Abilities (above)—the implementation of this change could have been to have these abilities deal 1 ability damage.