Star Trek attempted to give verisimilitude to the show by basing the ship's culture on naval military structures, officers, and lingo. The proper expression is "you have the CONN." TNG was consistent in using "CONN" not "COMM." However, Shatner was famous for his mispronunciations of certain words, and he seems to use "COMM" rather than "CONN." In true seamanship lingo, there is no such statement as "you have the COMM"--the idea that this is short for command is incorrect.
Others have already clearly described what "you have the CONN" means in seamanship, but it is true that Star Trek often seems to use "CONN" to mean command, though at other times it seems to just refer to control of the bridge, referring to the more traditional meaning of the steerage or helmsmanship of the vessel. If Kirk or Picard is just going to his quarters, the meaning is clearly closer to the traditional one whereas if the captain beams down to a planet, the term "CONN" seems to refer to something more like "command." Scottie clearly makes command-like decisions when he has the CONN when Kirk is on a planet surface, though he still operates within the Captain's orders. In any case, fiction can take liberty with these terms in ways actual seaman would never do; but the original expression is CONN, not COMM.