Re: but this can't be true
Granted the terminology varies across subjects (eg. epistemology, maths, logic...) and local usage, but equal and identical are generally understood to be two distinct relationships. That's why we use the two different words.
Generally two items are equal in some respect or property if they evaluate to give the same result in that respect, usually for a specific input.
Generally two items are identical if they are equal in all respects, ie. for all inputs and all variables, and are therefore functionally indistinguishable.
A kilo of apples and a kilo of gravel are equal in weight, for instance, but they're certainly not identical as you'll discover if you try to eat a gravel crumble.
Biting the hand that feeds IT
