Death's Dance has always given 15% physvamp (although now it gives omnivamp), you may be confusing it with the damage delay ratio, which is 30% and may have been nerfed from 35% at some time.
Lifesteal is a specific kind of "-vamp" (Which is any kind of direct "healing on damage" effect, such as what is gained from DD, Vlad's Q, or Nasus's passive, but does not include regen effects such as Soraka's Q, which is triggered by dealing damage but is not a -vamp effect) that applies only to autos and certain auto modifiers (Such as Nasus's Q stacks). It must be something inherent to the auto or AA enhancer, meaning, for example, RFC does not give you healing from lifesteal.
"Damage heals for %" is what is more commonly known as "omnivamp". It means any damage originating from that champion heals for that percent of damage dealt.
What Death's Dance used to be is physvamp, which is like omnivamp but only heals on physical damage, rather than all damage. Currently this only exists on
and its lesser variant.
Lastly, there's spellvamp, which is healing from any damage dealt by abilities (so anything that originates from the champion that lifesteal doesn't heal you on). Contrary to what some believe, it heals on both physical and magic damage, so long as it is from an ability, not an auto (Or anything that already heals from lifesteal). The only remaining source of this stat is the Ravenous Hunter rune.