Back in the days before Star Trek came along, when you used the term "to warp a ship" it meant to haul a ship through a restricted space by using lines attached to a fixed point, such as an anchor or pier.
Now, of course, "warping a ship" means to send it across space at near lightspeed by causing the space around it to "warp" at faster-than-light speeds. It was a clever bit of handwavium when Gene Roddenberry came up with the idea, and sort of thumbed his nose at Albert Einstein's relative speed limit. After all, a space opera needs to be able to have its ships visiting distant, exotic worlds, not plodding along empty interstellar space while the crew is in coldsleep.
Well, the goggle-eyed kids who fell in love with Star Trek have grown up into goggle-eyed astrophysicists working for NASA, and one of the let's-make-it-real tricks on their bucket list is warp drive.
And NASA's going along with them.
Personally, I'd rather have the transporter.