A tunnel through space-time joining two distant points, usually unstable and short-lived, whose one known stable example near Bajor made Deep Space 9 the most strategically important station in the quadrant.
A wormhole is a shortcut through space-time with a mouth at each end, allowing travel across vast distances in moments. Natural wormholes are almost always unstable: their ends wander, and they may collapse without warning.
Star Trek: The Motion Picture shows one created by accident when the refitted Enterprise's unbalanced warp engines throw it into a wormhole effect. In The Next Generation, The Price concerns the Barzan wormhole, auctioned as stable until its far end is found to move, stranding two Ferengi in the Delta Quadrant, where Voyager meets them in False Profits.
The great exception is the Bajoran wormhole, discovered in Emissary, an artificial and permanent passage to the Gamma Quadrant built by the Prophets. Voyager also meets a micro-wormhole in Eye of the Needle and a hidden one sought by refugees in Counterpoint.