Canceled and Expired are both permanent off market statuses. Once a listing is marked as either, it will remain that way permanently. Canceled listings do not switch to Expired (or vice versa), even when they reach their expiration date- they will continue to show as Canceled forever.
The major difference between the two is that a Canceled listing means that the seller has canceled their contract with the list agent, whereas an Expired listing means that the listing contract has run its entirety and has reached its expiration date.
Both statuses are equally easy to search for and see within the MLS.