gzip

As verbs the difference between compress and gzip

is that compress is to make smaller; to press or squeeze together, or to make something occupy a smaller space or volume while gzip is (computing) to compress using the (gzip) program.

As a noun compress

is a multiply folded piece of cloth, a pouch of ice etc, used to apply to a patient's skin, cover the dressing of wounds, and placed with the aid of a bandage to apply pressure on an injury.