Thanks for the suggestion. The general tying sequence is indeed similar. In that illustration, where the adjoining rope first crosses itself, if it had passed under instead of over, it would have been the same as the hitch I'm asking about.
But even if it would not surprise you if a similar-looking knot had similar performance, I'm guessing it would also not surprise you that similar-looking knots can sometimes have significantly-different properties. In this case, on the ropes I have here, the Sailor's Hitch seems to be more prone to capsizing, it isn't as effective at self-tightening under a load, and doesn't release and slide as easily. Whatever merits the Sailor's Hitch may have for tying onto a rigid member, it would appear to be not so good as an adjustable slide-and-grip hitch. So I'm hoping the hitch I'm asking about has its own distinct name, as I wouldn't want to use a name that leads people to a less-suitable knot.