I am reading "equivalence" too strictly (like "as a substitute"), because this is part of the documentation :) and I agree that in ordinary speech I would use it rather in the sense of “similar”.

In order to make sure, that everyone agrees only on that this requires only a documentation change? Because as for me, I think that it will better for `os.path.isdir` to raise `ValueError` or `DeprecationWarning` - `False` on empty string is not well defined behavior. But I'm fine to be alone with the last one.