Hope this is the right forum to ask this question.
Browsing through bicycle adds I’ve noticed there are two different designs of seat stays: one where the seat stays are directly welded on to the seat tube and the other one where there’s an additional tube running down from the seat tube at the same angle as the seat stays do which is joined to the seat stays right over the wheel (please have a look at the pictures). The latter looks to me like some sort of rear version of the front fork. Is there any practical difference between them or advantage of one over the other? If that matters, I’m looking for a bicycle to be used as/converted to a commuter/touring bicycle.

top is called fastback and the one with the single tube is called a wishbone. The wishbone was invented to cut costs. There is no difference in the utility of the bikes.

How does wishbone cut costs?

I used to paint John Cherry frames. He liked to do a wishbone style. The lower part of the stays below the wishbone he made out of straight gauge !/2" tubing (obviously saving money over tapered tubing). He would make these in batches including the wishbone and single tube no matter what the size of the frame. The single tube above the wishbone could be mitered to length and angle after the rest of the frame was made to just fit that frame. Doing one miter and fillet brazing it to the back of the seat tube (with a necessary reinforcement) saved time over prepping and brazing two seat stay tops.

There are far more important design aspects that will make or break a bike's intended use goal then whether the seat stays are full length of stop at the mono stay. Like fender clearance, rack mounts, cable routing paths.

I would also suggest that third and forth stay designs exist. The very common side of seat cluster attachment (as many millions of bikes have had for decades) and the Helenic (or as GT calls it, Triple Triangle). Still these don't really effect the bikes performance if all the more important details are done well.

I'm of the opinion that this stay stuff is far more about aesthetics and branding (see GT) then any structural aspect. The one possible exception might be aero drag reduction with a mono stay. Of course if the rider forgot to shave that day they just blew off any aero advantage Andy

It simplifies manufacturing. The seatstays can all be the same length, regardless of frame size, and straight-cut rather than mitered. The wishbone length varies with frame size, but only requires a single miter to join the seat tube.

Don't they still need mitered to join the larger tube?

Yes the top of the SS will need joining to the mono stay tube somehow. Often with a rear version of a fork crown. But it's the ability to produce a single spec sub assembly ahead of need that helps make a mono stay slightly less costly for production bikes. (Instead of the 5 or 6 different sized SSs needed for the bike's available sizes). Andy

You'll never see a bike with the wrong seat stays on it, like with some Treks.

I have a Grandis where the signature at the top is transposed left to right, it reads upside down.

There are plenty of "simplifications" seat stay top plugs were common but not commonly known in the 70's.
(think Colnago Super)
First wishbone seat stay example I saw was on a Freddy Parr built bike. Not that he was the first, just not common at all in the 70's.
Brian Baylis related that upon looking at Brian's Eisentraut A, Falerio dismissed it out of hand, as the seat stays were not brazed to the frame in the as he saw it, in the correct manner.

That's pretty funny, Eisentraut made all the Europeans look like hacks.

We had a bike in the boss's collection with a mono stay, employing a spring for a Moot's like suspension about 75 years before Moots was a brand. The bike was a shaft drive Columbia. So many bike ideas have been done so many times before. Andy