For the lane (and not champion type), a support is a champion that contributes to team success on a lower reliable experience and gold budget than the rest of the team. When optimized, this usually means preferring items with higher gold efficiency over slot efficiency, as well as playing champions that have innate base stats or utility.
Specifically note that most item goals in this game involve multiplicative scaling. For physical damage, you have AD, AS, crit chance, crit damage, Lethality, and %ArPen. For magic damage, you have AP, MPen, %MPen, CDR, and lots of active damage items. For defense, you have health and armor/MR. Utility items usually have large benefits that don't contribute to multiplicative scaling, making them gold efficient (useful even without other items) but less slot efficient (not as useful when you're full build as other options).
But that's all defining what makes a champion do well in the support lane.
So really what lines someone as a "True" Support?
To me, a support is someone who takes the above information and runs with it. You see the lower budgets as a challenge for finding out the best way to help your team.
Sightstone's an easy win because the utility it provides for its cost is unmatched, at the cost of poor slot efficiency. Supports don't need to rush Sightstone every game, but someone that doesn't get it fairly early most games is probably not a "true" support at heart.
But beyond that, the sky is the limit for supporting.