Although not as sporty as "endobetween" and "exobetween", mathematicians generally use the adjectives "closed" and "open" to describe the inclusion or exclusion of endpoints in an interval (range) of real numbers.
Thus $(0,1)$ is an _open_ interval, excluding (not containing) the endpoints, and $[0,1]$ would be the corresponding _closed_ interval resulting from including both endpoints.
Another paradigm from mathematical terminology would be that used of inequalities, namely strict (excluding the boundary/equality) or weak (including the boundary/equality). Thus `IsBetweenStrict` should be expected to reject the endpoints, while `IsBetweenWeak` should be expected to accept the endpoints.