Certainly not, but there is no redefinition that is anything more than gobbledygook. Look at the very definition you gave: That's not a unique or different way to write tests. It's not even a testing pattern in concept. That's just programming in general. It is not, for example, unusual for you to use an alternative database implementation (e.g. an in-memory database) during development where it is a suitable technical solution to a technical problem, even outside of an automated test environment. To frame it as some special unique kind of test is nonsensical.
If we can find a useful definition, by all means, but otherwise what's the point? There is no reason to desperately try to save it with meaningless words just because it is catchy.