[jfengel]

It means that it shares some, but not all, aspects of a social relationship.

It's often applied to one-sided relationships with celebrities, where you feel a personal connection to them but they literally don't know you exist.

[cess11]

Social relationship is much broader than human connection.

If I fall in love with Harry Potter, is that a human connection?

[jfengel]

The term "parasocial relationship" is usually reserved for actual people. You could stretch it to include fictional characters, but it misses out on some of the reasons we coined the term.

For example, you can't stalk Harry Potter. There are surely people stalking JK Rowling, and that is a better example of a parasocial relationship.

Not all parasocial relationships are pathological. It's just a useful extreme to illustrated why the distinction exists.