[Splat]

But those are the same things that they said experience would benefit (jumping, run-speed, dig-speed...)

Apart from the potion bottle, I would think it was more to do with experience.

There's a list of potion effects on the wiki and several of them are already caused by other things. There's the one that speeds up hunger drain - food poisoning from rotten meat - and one that caused damage over time - cave spider poison - and one that quickly heals health and hunger -golden apple - amongst others. So evidently not all potion effects are going to be caused by potions.
I get the idea that 'potion' is more a word meaning 'things that effect the basic mechanics of the game'. Some of the effects are caused by items or mobs. Some will surely be caused by experience. Others, like blindness and invisibility, remain to be seen (pun was not intended).