References aside, the distinction seems pretty obvious. A spell-like ability is like a spell, but it isn't actual spellcasting. (If it were the same, it wouldn't have a distinct name.)
If some PrC requires that you possess a pumpkin, you cannot get in by possessing some random gourd, even if it is a "pumpkin-like fruit".
Well, when it says you have to be able to "cast spells," it's a little hard to see why something which is neither cast nor a spell would qualify. I don't think anybody needs to make the case that it doesn't until somebody makes the case that it does.