Cheddaring is a unique process in making Cheddar cheese and you are quite correct, note ‘unique’ not processed in the way they make this cack.
So calling something Cheddar that isn’t made the way Cheddar is made is mislabelling it and yes there are other manufacturers of good quality Cheddar.
Over forty percent of the Cheddar cheese sold in the UK is not made here and not made to the exacting standards that real Cheddar is made here, it also tastes of beggar all in comparison to the real thing IMHO.