Why? Why is it so important that they be seen as the same thing to you? What benefit is gained from it? What benefit is gained from blending together a data structure that is fixed bit size from a family of data structures of variable size, a fairly fundamental difference? What benefit is gained from failing to consider the fundamentally different uses they are put to? What benefit is gained from looking at someone list a set of differences between the two, and basically saying, "yeah, they're different, but what if not?"

I can name further properties that differ between them. All sum types can embed arbitrary other existing sum types within themselves, without practical limit. Enumerations can not, because A: they may collide on which numbers they use and B: even if you remap them, you can run out of integers, especially with smaller values like byte-sized enumerations. Enumerations may have further structure within themselves, such that particular bits have particular meanings or values a certain number apart may have relationships to each other, or other arithmetic operations can be given some meaning; sum types themselves do not generally have any such relationships. (At least, I've never seen a sum type in two clauses of the sum type are somehow related; that'd be bad design of a sum type anyhow. Even if you did this to an internal integer contained in a sum type, it would be that integer composed in to the sum type that had that relationship, not the sum type.) Sum types have a rich concept of pattern matching that can be applied, enumerations generally do not (some languages can do some pattern matching with bits but there's still no deep structure matching concept in them).

I mean, how many differences are necessary before they are not the same thing? They can not fit into the same amount of memory; one is fixed in size, the other highly variable. One is simple to serialize into memory, the other has lots of complicated machinery. Each has operations generally valid on one but not the other (enumeration, pattern matching, sum type's composition whereas enums can not generally). The range of valid values (or domain, whichever you prefer) is not the same. There are languages that have enumerations without sum types, in that enumerations appeared in mainstream languages decades before sum types were a mainstream conversation. In what other ways could they be different?

It strikes me like arguing that ints and strings are the same, because honestly, what's the difference between 11 and "11" anyhow? Even if you're working in a language that strives to make the distinction as small as possible, you're still going to get in trouble if you believe they really are completely the same thing. And any programmer who goes through like truly thinking 11 and "11" are the same thing is in for a lot of confusion as concepts they should be understanding as separate, even if at times superficially related, are actually the same.