Budder is an iso extract BudderKing sells.
Kids on forums have attempted to reverse-engineer BK Budder by doing various little things to BHO and calling it Budder, but all they really have done is create confusion, because the real Budder product is very specific. Budder is made with specific strains (only BudderKing knows what they are).
Budder is a proper noun, it is not a generic word like hash. At least it wasn't until people started confusing it with BHO. Language being dynamic, now Budder is budder is Budder.
Budder has actually been lab tested, and it is widely believed to be the strongest cannabis extract to date. BHO with or without air whipped into it is also strong, but it is not the original Budder, it's just one of the many attempts to emulate Budderking Budder.