Both are different Chains. Oz was created by Lacie when she brought the twin rabbit dolls into the Abyss as a child, giving him life. The Intention of the Abyss then changed Oz's remaining doll-body (following the decay of the Earth-bound one) into the Chain, B-Rabbit, which she gave the ability to sever the Chains that prevent the world from falling into the Abyss. Jack then Illegally Contracted to Oz and after severing the Chains and killing many Baskervilles (including Oswald) Oz was tormented. Unfortunately for Jack, Oswald had used Raven, Owl, Dodo, Gryphon and Jabberwock to mend the Chains, and so he went to Alice to have the Intention help him sever the Chains once again.
Alice was in control of her own body however and wouldn't allow the Intention to help Jack, committing suicide in order to stop the Intention from being forced to help Jack. The Intention then used Alice's body to form a connection with Jack's body in order to reach Oz so that she could have Oz destroy her memories so that she would be unable to help Jack again. Alice prevented this however by joining with Oz to become Alice the B-Rabbit, simply inhabiting Oz's body with her soul.
Meanwhile Lacie's Chain, being the original, was just the inspiration behind the design for Oz's Chain form. No further information about the two B-Rabbit's has been given.