So spell vamp isn't about Magic/Physical/True damage, but rather about "Abilities." The term Abilities here is meant to be distinct from "Auto-Attacks" (which benefit from life-steal). With a few notable exceptions all attacks fall into one of these categories: Auto-Attacks or Abilities.
Now it's worth noting that there is a class of abilities, "On-Hit," which are not clear as to whether they fall into the "Auto-Attack" or "Abilities" category. Some of these will benefit from life steal (eg. Blitzcrank's Power Fist), some will benefit from spell vamp (eg. consuming a mark from Akali's Mark of the Assassin), and some will benefit from neither (eg. Irelia's Hiten Style), though the auto-attack portion will still benefit from life steal.
A full list of these abilities can be found here: leagueoflegends.wikia: On-Hit_effects