Optional processes are flow rules (life cycles for data) that can be called and processed in parallel with the original flow. For example, a user may start an investigation into a credit card charge while he/she is on the phone helping the customer with a lost card. The investigation will run even after the lost card is closed.
Local Actions open and are generally completed and closed and the user returns to the same place. An example might be the user opens a local action to see the charges made on the credit card while on the phone with his/her customer. there are no charges, the window is closed and the user continues to process the lost card.