The parties in a protocol are the identity owners involved. In a protocol where Alice introduces Bob to Carol, the parties are Alice, Bob, and Carol.
The roles in a protocol are the perspectives that parties take on an interaction. In an auction protocol, there are only two roles--auctioneer and bidder--even though there may be many parties.
The participants in a protocol are the agents that actually move the steps of the protocol thorugh the interaction. Alice, Bob, and Carol may each have a cloud agent, a laptop, and a phone; if they engage in an introduction protocol using phones, then the agents on their phones are the participants. If the phones talk directly over bluetooth, this is particularly clear--but even if the phones leverage push notifications and HTTP such that cloud agents help with routing, only the phone agents are participants, because only they maintain state for the interaction underway. (The cloud agents would be facilitators, and the laptops would be bystanders). When a protocol is complete, the participant agents know about the outcome; they may need to synchronize or replicate their state before other agents of the parties are aware.