You may have a situation where you have positioned one region over another, and you just want to cut the lower region so that it directly adjoins both ends of the overlapping one, with no overlaps. To do this, select the upper region, then choose Edit > Separate > Separate Under. This will split the lower region so that it no longer overlaps the upper region at all.
Here is an example where we start with a short region placed so that it overlaps a longer region:

When we perform the Separate Under edit, the lower region splits in two, with boundaries exactly positioned at the edges of the upper region:

If the upper region covers only one end of the lower region, then this operation is equivalent to Trim to Next or Trim to Previous, depending on which end is covered.