Riiiiight...

I won't be cruel and unusual in my post, but I will tell you one thing: I want to be.

Kingdom Hearts, to my knowledge, takes place in some alternate dimension, and on top of that, has a different timeline. The two games share characters and the many of the characters' trademarks, but that is it. Nothing more.

Aeris is a mistranslation of Aerith. Square realized this in their later games, and as such, whenever Aerith is mentioned, it's spelled Aerith, as it was originally intended.