Saga is a keyword always used in combination with CQRS. There is something needed to take care of the business rules of multiple bounded contexts and/or aggregates. In some case this can be done without a state but in the most cases a state is needed.
So why is now the name so relevant?
You should focus more on the idea than on the name. Process Manager can be explained much simpler compared to SAGA. This is primarily the reason Greg uses this convention.
There is no CQRS framework without SAGA. Never seen a Process Manager in such a framework.
actually, they are intended as synonyms. The problem here is that the term Saga actually predates CQRS (a paper about it was published in 1987) and has a subtly different meaning. Therefore, the term Process Manager is more commonly used nowadays. Axon still uses the term Sagas.
Essentially, in Axon, a Saga is a stateful event handler. The scope is defined by so called association properties, which tells Axon which instances should be triggered by which Saga instance.