“Paxos” is a term that can mean many different things, so it’s better not to get too attached to any one meaning especially in different contexts.
Multi Paxos is commonly used (especially in industry) as short hand for multi decree Paxos (in contrast to single decree Paxos), but “Paxos” most often refers to the family of protocols, all of which are typically implemented with a leader. It is confusing of course because single decree Paxos is used to implement EPaxos (and its derivatives).
It’s worth noting also that Lamport is (supposedly) on the record as having intended “Paxos” to refer to the protocol incorporating the leader optimisation.
Multi Paxos is commonly used (especially in industry) as short hand for multi decree Paxos (in contrast to single decree Paxos), but “Paxos” most often refers to the family of protocols, all of which are typically implemented with a leader. It is confusing of course because single decree Paxos is used to implement EPaxos (and its derivatives).
It’s worth noting also that Lamport is (supposedly) on the record as having intended “Paxos” to refer to the protocol incorporating the leader optimisation.