Completed or Completed :-)

In a ticket:

Is there any difference in clicking the button Completed versa using the Ticket status dropdown list, and choosing Completed ?

The result is the same. Yet, clicking Completed button changes the status and also saves the ticket while with status field change it'll only be actually modified and considered completed when the ticket is saved.

In both cases the before-completion checks, as defined in Tools > Options > Tickets (Admin) tab, will run once the ticket is saved.