What is the difference between a constituency and a region?

A region is a geographical area, defined in some fashion that is sometimes very specific and sometimes very general.

A constituency can be one kind of region. It is the region from which all voters vote to select who will hold a specific elective office.

Sometimes a constituency is a theoretical region not tied to geography. This is the case when we talk about a politician or leader whose constituency is all people of a particular background, or shade of opinion.