The semantics are different; the emphasis is different, etc.

Different semantics: Fan means follower or supporter, usually referring to a firm supporter of something, including both pursuit of people and love for things. Fans specifically refer to ardent supporters of public figures such as celebrities, singers, and sports teams, and usually only follow specific people or teams.

The emphasis is different: fans place more emphasis on continued support and loyalty to something, while fans place more emphasis on fanatical love and pursuit of a certain public figure.