Word for the opposite of "overlap"?

I'm looking for a nice, elegant word to describe the part where/extent to which things don't overlap.

"Discongruity"/"discongruence"/"incongruity"/"incongruence"/"complementation"/"complementarity" get sort of close, but I'd like other ideas. (The tighter the relationship with "overlap," the better!)

Note that words like "exclude" add meaning undesirably. "Diverge"/"differ" are not as specific as I'd like.

SAMPLE CONTEXTS:

"A group which [---]s completely with/to the other group" (i.e., "has no members in common with" from within a broader group to which they both belong).

"The [---] between this concept and the other is" (i.e., the part that not only differs between the groups, but specifically differs in the manner of "sticking out" from one group in one way and the other in another.)

Solution 1:

What you have is two sets that are disjoint: they have no elements in common.

If you are talking about spatial regions, you can also say that the regions are not contiguous, or discontiguous, which means that they do not touch (overlap).

• "A group which is completely disjoint from the other group" means precisely that the two groups have no members in common.

(I don't understand your second example, in particular "sticking out from one group in one way and the other in another.")

Solution 2:

Separate, mutually exclusive, nonintersecting...

Perhaps you should give more context or an example sentence? I'm not sure how you are using the word/phrase.

Solution 3:

If you need to be very precise, there's always nonoverlapping:

adj. that does not overlap

(Collins Dictionary)