Oddly enough, a simple term might help. Friends-with-benefits. I don't see it used in terms of established relationships and poly very often, but I can see how it fits what you're looking for. It's something my wife and I have dealt with.
A friend you can connect to, hang out, go to movies, play video games, see your kids play together, chat about life, anything everything etc. And yeah, at times, when sex happens, it happens and is a good, non-weird thing.
FwB can give you that long-term sincere connection (if they are/become a close friend) without the restrictions of a relationship (expectations).
This is used so casually typically that it may not be the best idea. I don't see it as the same as a booty-call.