I don’t know if this really counts as a spin-off, as it was just a retooling of the first show, but the hour-long drama Tattinger’s became the half-hour sitcom Nick & Hillary.
ALF, the half hour sitcom, spun off ALF, the Animated Series which as well as being animated, was also pseudo-science fiction. It also spun off Alf’s Hit Talk Show, which was a talk show with ALF as the host and Ed McMahon as his sidekick.
If we categorize Doctor Who as a children’s show, Torchwood isn’t.
If we don’t consider Doctor Who to be a children’s show, The Sarah Jane Adventures is.
The encyclopedic knowledge of the collective Dope is always impressive. Just think if we could harness this for good. 
In the mid 1990s the Cartoon Network aired *Space Ghost Coast to Coast *, which was a talk show hosted by the the 1960s Hanna Barbara cartoon character Space Ghost.
Star Wars was a space fantasy adventure. The Star Wars Christmas Special… wasn’t.
There is no Star Wars Christmas Special. Keep telling yourself that.
If we’re making a course change towards movies, I’ll add Alien, a haunted house movie in space, and Aliens, a sci-fi action movie. In space.
And relating to the above, there was Highlander, a fun cult-classic, and Highlander 2, a movie which doesn’t exist.
1977’s Fernwood2Night was a farcical “talk show” that sprang from the semi-serious/semi-absurd send-up of soap operas, Mary Hartman Mary Hartman.
Also, if Doctor Who is a children’s show, The Class isn’t. If Doctor Who isn’t a children’s show, K-9 is.
It was, but it wasn’t a different genre, just a different emphasis. The Lone Gunmen was on average more comedic than The X-Files, but elements of The X-Files, and even a few entire episodes, were at least as intentionally comedic as The Lone Gunmen. And The Lone Gunmen wasn’t really a comedy - it was a conspiracy thriller with a lot of intentionally comedic elements.
Could Sesame Street be considered a spinoff of The Muppet Show (or vice-versa; I’m not sure of the starting dates)? I’d say that a comedy variety show and a pre-school educational show are different genres.
Sesame Street seriously predates the Muppet Show - 1969 vs 1976.
But!
Neither of them is the ‘original’ show - that would be Sam and Friends, from 1955, which is where Henson first started using the Muppets - including Kermit (though, not a frog, yet).
Sam and Friends was, as I understand it (I’ve only seen a couple sketches), more like the Muppets’ various variety show appearances (most of which also predated Sesame Street) and the Muppet Show, than it was like Sesame Street.
Nitpick - it’s just Class*. But your point stands.
(IMO, Doctor Who, in its current incarnation, is a family show, not a kids’ show, so all 4 spinoffs - the adult Torchwood and Class, and the definitely kiddy Sarah Jane and K-9 - count, if you’re going to count demographic as part of ‘genre’.)
- IMO, it was the best of the spinoffs (though I haven’t seen any of K-9, so I can only say it’s the best of the three I’ve seen), and it’s a huge injustice it didn’t get a second series. (Not that I thought Torchwood or Sarah Jane Adventures were bad, on the whole (though Torchwood had some episodes that were), just not as good as Class.)
Then there was the less-remembered, but just as insanely brilliant, Cartoon Planet, which featured Space Ghost, Zorak, and Brak performing songs and sketches and other weird stuff. It made zero sense, but was hilarious.
Also from Adult Swim came Sealab 2021, a very funny, silly, and sometimes surreal animated comedy that was a… Spinoff? Reboot? Continuation? Parody?.. of the earnest and decidedly unfunny Saturday morning cartoon Sealab 2020.
Max Headroom started out as a short TV movie, then was spun off into a DJ for a music video show, then returned back to an ongoing series based on the original short film, some roles partially recast.
And the best theme song, ever, all 27 seconds of it!
Muppet Babies was an animated version of The Muppets as toddlers .
I seem to recall a drama, Trapper John, which I took to be a spin-off of MASH.
There was also Harvey Birdman, Attorney at Law which was a comedic remake of the “serious” cartoon Birdman and the Galaxy Trio.