> and that which they are not is precisely the domain of the other word
External relationships are a thing, which are in neither of those domains.
An intramural activity is not the same thing as an intermural activity, but the overwhelming majority of activities which are not intramural activities are not intermural activities either, most are extramural activities.
> External relationships are a thing, which are in neither of those domains.
They are a subset of inter-, pretty obviously.