It's complicated by the fact that larger organizations/cities/etc. can be effectively agglomerations of smaller entities with tighter or looser coupling. But, yes, in general.
You can see some of this in your examples.
US DoD is, of course, actually part of the US government but relatively few DoD employees ever really interact with people in other US government branches. Ditto with Walmart store employees and the "mothership."
Voting for a position at the government of my ~3M people city is completely different from voting for a position at the government of my ~300M people country.
Logically, it makes sense that the situation keeps changing. But it still feels weird. How many different kinds of relationship are we capable of?
> How many different kinds of relationship are we capable of?
Kinds? (qualitative) ...
... I think you very much upped the ante there :)
I'd posit a (cheap, easy) guess: Infinite.-
PS. Of course, taking the "cheap" way out in thinking about this of assuming each one-on-one relationship (not to mention one-to-many, and many-to-one and many-to-many, like mentioned upthread) to be a unique "kind", is an easy way out: As many types of relationships as people, because no two people are alike, and so is their relationship. Heck, considering each of the individuals (themselves) involved, might subjectively experience a different relationship, there's even a "two to each pair" pairing of relationship types to participants, to be considered ...
Now, when, IMHO it gets interesting is if we - a bit more rigoroulsy - attempt a "taxonomy" of relationship "types".-
(And, then, again, I am sure anthropology has studied and catalogued those to death ...)
... and different organizations, of course.-
Leaves me wondering - among many things - what the "largest qua payroll" organization worldwide might be.-
US Dept. of Defense, Chinese PLA, Indian railways. Walmart, Saudi Aramco come to mind.-