I suspect that these are indeed two different men, but unfortunately the "man-of-war ship" story is just family tradition. The Early New England Families Project wouldn't give me access with just a guest account, so not sure if they have any hard proof that John (son of Samuel Dudley) died relatively young in Massachusetts.
I found it very interesting that John of Guilford Connecticut was called "Deadly" in the early records and only changed to Dudley later. Anyway, the following seems to sum it up:
Records indicate that John Dudley lived with his grandfather, Gov. Dudley, as a young boy and later disappeared. Some say he died (no proof of this), but others say he ran away and later appeared in Guilford with old friends of his grandfather's, who had died by then. There are no ship records showing the arrival of an adult who could have been this John Dudley. However, another story says that this John Dudley had been impressed to serve on a ship in England and escaped years later in Boston. He then made his way to Guilford, where he worked for Thomas French, later marrying Thomas' daughter, Martha. His name, in early Guilford records, was spelled "Deadly", but later "Dudley." John is the pivotal point for claiming lineage with the Dudley and Winthrop lines. I have included him in the Dudley and Winthorp lineage, but keep in mind, there is no proof.