Commonly used to emphasize variety within a category without specifying every possibility. At the fair, there were games of one kind or another for everyone.
Pro Tip 2/3
Context Matters
It may suggest a lack of concern for the specifics, focusing instead on the overall concept. They were discussing politics of one sort or another.
Pro Tip 3/3
Implies Diversity
Highlights the presence of different types within a single subject, but not necessarily a large number. The workshop tackled issues of one kind or another.