Semantics. Spec is very close to dependent types. "Entirely different purpose" is kinda vague. If the end result is the correctness of the program, the purpose is the same.
If someone can perform Vivaldi's Four Seasons on Ukelele, it's cool. It doesn't make Ukelele less of an instrument.
If we look at programming languages like Java, Typescript, C++, Haskell, etc., then we see that their type systems are completely different and have an entirely different purpose. Claiming to those users that spec is a type system, is just misleading them.