A Hazelcast Jet instance is a unit where the processing takes place. There can be multiple instances per JVM, however this only makes sense for testing. An instance becomes a member of a cluster: it can join and leave clusters multiple times during its lifetime. Any instance can be used to access a cluster, giving an appearance that the entire cluster is available locally.
On the other hand, a client instance is just an accessor to a cluster and no processing takes place in it.