Once you command your Sim to formally introduce themselves to the target, all normal social interactions become available. In that way, you can interact with your fans without adding another entry into your relationships panel. You do get some special interactions, such as being able to sign autographs for fans, that can be executed before your Sim formally introduces themselves to the target. As the player-character, you can command your Sim to do anything you want even for the normal Sims of the world. In general, this inequality of interaction doesn't work both ways.
Of course, the celebrity may decline your Sim's advances anyway if there is not a social foundation for them to be friends!
Your Sim can even enter romantic relationships or request a celebrity to move in with them. Once your Sim reaches or surpasses a celebrity's level, interactions can happen as normal as seen with Vanessa Jeong earlier.
