Make shift Available allows other employees assigned to the same location and position to see that the shift is available for pickup. Employees can apply for the shift and then a manager approves or denies the exchange.
Offer shift allows an employee to offer the shift to a specific employee who works the same location/position. This also works in a trade situation. Both employees offer their shifts to each other to complete a swap.
However, in both situations, if no one applies for the shift or accepts the shift (or an application for it is denied by your manager), the employee who was originally assigned to the shift is still responsible for working it.