The difference in these relationship dynamics can be stated in terms of power. In her relationship with John Proctor, Abigail has far less power to influence his behavior than she has in her relationships to the other girls. This difference can be seen rather clearly in the first act of the play.
In the first act Abigail runs the group. She instructs Betty, Mercy Lewis and Tituba as well, telling them what to do to avoid punishment for what they were caught doing in the woods. Her authority is strong and aggressively enforced.
"[S]he forcefully insists that the girls stick to the story that they were only dancing and that Tituba and Ruth alone conjured her dead sisters. She threatens great harm to anyone who breathes a word of the other things." (eNotes)
In the same act, Abigail attempts to convince John Proctor to renew an affair with her. He refuses. This refusal is a large part of his power in the situation, but he also is older and was once her employer. With Proctor she is the supplicant seeking agreement and approval (albeit a demanding and threatening supplicant) and with the other girls she is a domineering and forceful authority.