Database clustering is a bit of an ambiguous term, some vendors consider a cluster having two or more servers share the same storage, some others call a cluster a set of replicated servers.
Replication defines the method by which a set of servers remain synchronized without having to share the storage being able to be geographically disperse, there are two main ways of going about it:
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master-master (or multi-master) replication: Any server can update the database. It is usually taken care of by a different module within the database (or a whole different software running on top of them in some cases).
Downside is that it is very hard to do well, and some systems lose ACID properties when in this mode of replication.
Upside is that it is flexible and you can support the failure of any server while still having the database updated.
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master-slave replication: There is only a single copy of authoritative data, which is the pushed to the slave servers.
Downside is that it is less fault tolerant, if the master dies, there are no further changes in the slaves.
Upside is that it is easier to do than multi-master and it usually preserve ACID properties.
Load balancing is a different concept, it consists distributing the queries sent to those servers so the load is as evenly distributed as possible. It is usually done at the application layer (or with a connection pool). The only direct relation between replication and load balancing is that you need some replication to be able to load balance, else you’d have a single server.