It sounds as if you're of the view that I/E, J/P and NT/ST/NF/SF are independent of each other.
Yes.
Many INTPs have reported they function as INTJs "at work".
I've noticed that I effortlessly shift to an ENTP stance when I'm around INTP friends.
If INTP and INTJ were different personality types, then they would have 2 different personalities, and would be 2 different people.
So if these people show both the traits of INTPs and INTJs, they would have multiple personalities in the same person, and thus would have Multiple Personality Disorder.
If they had MPD, then other people would see and react to the same symptoms as those of people with MPD. When their friends and family rang them at work, they would experience them as having a different personality and thus as a different person.
So more than likely, you're saying that some people have a personality that behaves like the stereotype of an INTJ at work and the stereotype of an INTP at home. Those people have the same personality, and thus the same personality type.
Ergo, the online descriptions of INTPs and INTJs that people read online and often assume are the nature of what it means to be an INTP or an INTJ, describe roles.
"Reciprocal roles" are the typical roles we use to decide how to behave in real life situations, e.g. student and teacher, parent and child, employer and employee, etc.
An absent-minded professor that works at a university and who is married, and whose wife and university take care of most of their basic needs so they can think about the big ideas and advance humanity, would be this sort of a role.
But this doesn't describe the personality, rather the way different types of people behave in different types of situations.
A person is the totality of set of the different ways they behave in different situations, e.g. when stressed, you behave one way, and when relaxed, you behave in another.
E.G. if someone is an INTJ at work when it matters and an INTP at home when it doesn't, that person is a person with a personality, and thus with a type of personality.