Resolution:
The difference between the "Save" and "Save and Process" button is as follows:

1: With worksupervisor role
Save: Modification of the record will happen and record confirms without going to the workflow.
Save and Process: Modification of the record happens and the record goes in to the workflow where it will be confirmed after the workflow.

2:Without worksupervisor role
Save: Modification of the record will happen and record becomes unconfirmed without going to the workflow.
Save and Process: Modification of the record happens and the record goes in to the workflow where it will be confirmed after the workflow.