Anything you create yourself is always labeled as potion or poison. Elixir, philter, draught, etc. can be only looted or bought.
Think of it as 'branding' - I could, with the right ingredients and such, make a burger that was pretty much identical to a Big Mac (and I could definitely make one that was way nicer), but only McDonald's can actually call their burgers Big Macs.
You can, with the right skill level, perks, and combination of ingredients (I think, anyway, that some produce a stronger effect than others, though that may be a mod I have) create potions that are a lot stronger than what you can make at the start, I can't remember if you can eventually make potions that are as strong as the strongest bought ones, I think it may depend on the type of potion, and you would probably also need to have the strongest possible fortify alchemy enchantment (which, I believe, the strongest one you can make is stronger than the strongest one you can find/buy, so if you want to make the best possible potions you'll also need to max your enchanting).