Persistent sequence generates unique numbers across the graph runs. If you run the graph more times, you will get a different sequence numbers in each graph run.

The persistent sequences use a sequence file. The sequence file contains data necessary to transfer sequence state across the graph runs.

Multiple graphs using the same sequence file can run in parallel.

Multiple different sequences can use the same sequence file, it has the same effect as if the same sequence is used.

You can even use sequences from a different sandbox. But make sure that the path to the sequence file is specified as absolute in the sequence configuration. (e.g. sandbox://MyProject/mySequenceFile)

The sequence in not safe across multiple Cluster nodes.