it all depends on which version of the term 'support' you're talking about. 'Support' in this game can be used to describe either a role or a position.
The support role pretty much is as you're interpreting it; those of the support role specialize in buffing/healing/shielding allies and preventing enemies from harming those allies.
The support position is just a name for the non-ADc in bottom lane. It's called 'support' mostly because the typical champs that used to be taken there were those of the support role... you know, back when ADcs actually almost had weak early games and needed to be babysat and protected. Of course, now that ADcs have been repeatedly given more and more safety nets both within their kits and without, their partner in lane doesn't really need to offer any kind of protection to them, and so the person occupying that spot doesn't really need to be of the support role anymore, but the name 'support' still sticks to the spot because... well, frankly, what else are you gonna call them? The ADc's bitch? The team pauper (although the jungler's giving them a run for their money on that accord)?
Leona and Blitz are called 'supports' because they get taken to the support position. Their kits aren't inherently supportive or protective, aside from having some cc for peel/lockdown (which just about any bruiser can cover... hell, Darius can legitimately peel better than Leona), they just get called that because of where they go, and (very many) people can't distinguish between the two uses of the word so they assume (incorrectly) that this means Blitz and Leona must be considered of the support role; they are not, they are merely bottom-lane tanks/bruisers.