For jobs, when making a change to a field under Approval Details, this will trigger the approval chain again.
Note if you are using 2-stage approvals and the job is fully approved, making a change to a field will trigger the second stage approval chain again.
If you would like to trigger the first stage approval (Approvals to start recruiting) again, you'll first need to set the job to Draft mode and then make a change to the fields under Approval Details.
For offers, only certain fields will trigger the approval chain again. You'll want to note which fields by the cross indicated next to the name of the field as seen here: