All you seem to be describing are a relationship where everyone lives together and one where they don't. That isn't a relationship difference, you just don't happen to live in the same place or don't want to. To me, I couldn't care less where my partners were living. It wouldn't change my relationship with them. I wouldn't love them more or less.
So in short, both are polyamorous relationships. Polyamory itself translates as "many loves" and describes nothing about geographical locations.
A good phrase I see over and over - "There are as many ways to practise polyamory as people practising it."
there is nothing weird about your wanting a triad. Many people are in one. I would personally suggest not actively looking for your "ideal" relationship though. Just letting things flow into where they want to be can be a good thing. Though if that is all you wanted and there's no way you would have it any other way then fair enough.
I hope you find what you're looking for and welcome to the forum.
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