Clarification of "Separate and Apart"

My wife and I live in a house that has a living area that is basically a separate apartment, with its own bedroom, bathroom, kitchen, etc. There are separate entrances in addition to a common door. The “apartment” has its own mailbox, so whoever is living there can receive mail at a different address. It could be considered an asymmetric duplex with a common entry.

If we lived apart in these two parts of the house would that in your opinion satisfy the “separate and apart” requirement?

Are there accepted definitions of what “separate” and “apart” (or “separate and apart”) actually mean?

Thanks

If you are not sharing a living space, that would be separate and apart.