You all are mixing your metaphors a bit. Wormholes “fold” space; imagine if the universe was a piece of paper. Now fold the paper in half and poke a pencil through it. That’s folding. “Warp” engines, like the Alcubierre Drive, do just what they say - they warp spacetime itself around the ship by compressing the spacetime behind the ship and expanding the spacetime in front of the ship, essentially creating a pressure differential that naturally pulls the ship along it’s new modified world line. This is what they’re talking about any time you hear them mention a “warp bubble”.