It varies and one should "never assume"

I have come across cases (in the Overton family) where Sr. was the grandfather of Jr., not his father.

I am told that there are cases where Sr. was an uncle to Jr, and the designations were used because they lived in same area and a distinction was needed between the two.

In my Johnston line my great great grandfather was John Waller Johnston (no designation after the name) and he died the same month his only son was born, also named John Waller Johnston. Later the younger one had a son of his own also named John Waller Johnston and at that point they started using the designations Sr. and Jr. (even though they were really the 2nd and 3rd in direct line with the same name).

There are now also a III and IV (even though they are really 4th and 5th in direct line with same name).