Two other examples:
1] 'The Dead Zone' - Once Greg Stillson became the Vice President of the United States (on his way to becoming the President), we left John Smith of Earth Prime-Time and instead followed his doppelganger in a new Toobworld.
2] 'Arrow' - For thirty episodes, this was a welcome addition to the main Toobworld, joining such shows as 'Batman', 'The Adventures Of Superman', 'The Incredible Hulk', 'Spiderman', 'Wonder Woman' and 'The Flash'. And it's because of 'The Flash' that 'Arrow' had to be shipped off to the comic book Toobworld where 'Lois & Clark' and 'Agents Of SHIELD' exist. There is only one Barry Allen for Earth Prime-Time and he's John Wesley Shipp. (Although it is cool that he'll be in the new 'Flash' series as Barry Allen's father.
'AS&J' had to be split into two different dimensions because of the untimely death of Pete Duel who played Hannibal Heyes aka Joshua Smith. The show's narrator, Roger Davis, was then brought into the show as the new Heyes/Smith.
For the record, I don't elevate one version over the other, even if I do prefer the Pete Duel episodes. But Roger Davis brings some excellent qualities to the role, especially a quiet sense of humor, and he does look as though he belonged in that time period.
I once tried to keep both versions of 'AS&J' in the same dimension with an elaborate blog post in which the reanimated corpse of Danny Bilson (aka "The Smiler") - brought back to life by Mr. Garrity - housed the the mind of Hannibal Heyes which had been transferred from his dying original body - by Dr. Loveless!
But it was all too complicated and was instrumental in getting me to subscribe to the mantra of Occam's Razor when it came to my televisiological theories.
Besides, it never took into account that each week we saw the earlier years of Hannibal Heyes and Kid Curry replayed out as though the Pete Duel version never existed.
That's a good deal?
What still needed splainin was why there was a marked change in the DNA of Hannibal Heyes in that alternate dimension and yet all the other characters looked as they did in those earlier episodes. Characters like Harry Briscoe, Big Mac MacReady, and of course Kid Curry/Thaddeus Jones.
If they had all been recast, I would have just tossed that second part of the series into the Land O' Remakes.....
The simplest splainin may still be complicated in the details, but here goes....
The opening credits of the show always referred to Heyes and Curry as "these two Kansas cousins". And I believe that's true - they were actually cousins... but not by blood.
In the preceding generation, Mrs. Heyes was either the sister to Mister or Missus Jones, or Mr. Heyes was the brother to Mrs. Jones. Either way, Mr. and Mrs. Heyes could not have children of their own and so they chose to adopt from a local orphanage.
In Earth Prime-Time, they adopted the baby who would grow up to be Pete Duel's Hannibal Heyes. "Over There" in the other TV dimension, their new-born addition to the family would one day be the Joshua Smith as played by Roger Davis.
Basically? The luck of the draw.
And since we saw Roger Davis in the original run of 'Alias Smith And Jones' as Danny Bilson, the deadly "Smiler With A Gun", it's likely that Heyes and Bilson were in that same orphanage in both dimensions.
This is not to say that the Pete Duel baby in that other dimension would be adopted by the Bilson family. And even if he was, there's no guarantee he would have grown up to have the same temperament and destiny as the original. In fact, he could have grown up to become a minister or a farmer.....
Happy trails to you!