Cancelled to order postage stamp is a stamp the issuing postal service has cancelled (marked as used), but that has not traveled through the post. Instead it got handed to a stamp collector or dealer.

Unused, has some disturbance from a stamp hinge.

Faint impression of a removed hinge over a small area

Unused, has full original undisturbed gum with no trace of damage done by a stamp hinge (also called "stamp mount", used to affix the stamp to a page of a stamp album).

Only if issued with gum

Used stamp that has traveled through the post.