The higher the grade on the potion, the more "rarities" it'll exclude, if that makes sense.

So at grade 100, you can only get items that have a rarity of 33% or lower. Be that eggs or decorative items etc! It's less of a chance that you'll get rare items, and more of a guarantee that you won't get more common items/eggs if you make a high quality potion.

Of course there is still some RNG involved as there are still items/eggs that have very low % so you can get technically unlucky and get a starter egg (30% rarity) even if you have a 100 grade potion, if you are trying to hunt for a legendary egg for example. So you shouldn't use a Rarity excluder by itself you should use it with a Pixpet Potion or a Decoration Potion.

And to answer your edited question -

Special Ingredients and Potion/Evobar Ingredients are just two different categories of items. Both are technically used in some evolution bars, but the biggest difference is that Special Ingredients don't have grade, but Potion/Evobar Ingredients do.

In the Special Ingredients category you have things like Feli Crystals, Vanilla Pods, etc. Potion/Evobar Ingredients are mostly all those liquid metal items.

The potions are just used to increase the chance that your pet specifically brings items of those categories back from hoards. c:

@Hopolites