They are more or less synonymous when speaking of a person's character
traits, but not if it refers to a physical disability, for example.
Suppose someone was born with six fingers on each hand. Suppose
we express surprise. That person might wonder why we hadn't
noticed before and say:
Didn't you know that I was just that way?
But that person would never answer:
Didn't you know that I was just that kind of person?
because this situation has nothing to do with having the character traits of a certain kind of person.
CJ