What is the difference between consensus and mutual exclusion in Distributed Systems? If we can achieve consensus, does it imply we can achieve mutual exclusion? Is there a difference?

Example : Paxos solves the consensus problem, can it also be used to solve mutual exclusion?
If you have a consensus mechanism, then you can achieve consensus on who owns a critical section, and thus solve mutual exclusion. This is exactly what happens in, say, single-master distributed database systems when they are doing leader election to decide which machine will accept writes (this has to be mutually exclusive).

However, different algorithms for mutual exclusion provide different guarantees of progress in the presence of failures; those that are fully fault-tolerant are essentially equivalent to consensus; those that aren't, are weaker.