I’ve been trying to think of bands and artists that caused others to copy their style and sound but who themselves moved on to sound different.
The only band I can think of is Radiohead.
The Beatles.
I was wondering about them. I wasn’t about in the sixties but I always thought their early sound wasn’t unique and they just did an existing style rather well. Maybe I’m wrong about that. Either way I guess their success would have encouraged a lot more new bands to adopt the style they had.
Bob Dylan multiple times in his career. He started as the gruff folkie with self-penned topical songs and spawned a legion of young men with acoustic guitars voicing their concerns (not that Dylan was the first folkie witn topical songs, of course not, but that’s another story). At that time, he turned to electric rock’n’roll with acerbic, sophisticated and often acid-drenched lyrics, and everybody in rock followed and was influenced by his electric trilogy of 65/66. When the rock revolution reached its psychedelic peak in 1967, he had already moved on to record the Basement Tapes with the Band and thus founded the music we today call americana, as also documented on his 67 album “John Wesley Harding” and culminating with 69’s “Nashville Skyline”, which was one of the starting points of country rock, which became one of the leading trends in the 70s. He was often far ahead.
Television was the progenitor of the 70’s NYC punk scene.
I wasn’t around then either, but my understanding is that the Beatles were unique when they first started. It just doesn’t seem like it now because so many other bands copied their style.
The Kinks.
Their early songs like “You Really Got Me” and “All Day and All of the Night” mark ground zero in the development of what became hard rock and heavy metal but it was nothing like nearly everything they did afterward.
There were precursors like the Everly Brothers, but the Beatles music stood out from the start, especially since music at the time was going in different directions (folk oriented and beach music).
The Grateful Dead evolved from a psychedelic rock group to something more country oriented with “Workingman’s Dead” and “American Beauty.”
In 1964, the Moody Blues were in the vanguard of the British R&B scene that dominated the Rock world throughout the late Sixties and early Seventies. With a lineup change in '66 they took a sharp turn toward Clasical/Art/Prog Rock and never looked back.
If ever the world needed a clone, it would be of Ray Davies. One to pioneer hard rock with his brother Dave, and the other to do all the cool psychedelic/nostalgia Brit Pop stuff.
This example doesn’t quite fit the OP’s question. But Joy Division is a pretty clear influence on subsequent goth or droning bands such as Interpol, the Cure, Bauhaus, Sisters of Mercy, etc. Upon the death of their singer Ian Curtis, they morphed into New Order, which went in a completely different direction (electronic dance music).
Cream
Established the equally talented Power Trio as a thing [in rock] (though it was long a standard in jazz) then moved on by disbanding.
For those who are yelling that The Jimi Hendrix Experience was also a Power Trio, Hendrix far outdistanced Noel Redding and Mitch Mitchell in talent.
David Bowie isn’t a band, but he deffo spawned copycats, while quickly moving on with his own music, re: Glam Rock etc.
I came to say this, but I couldn’t have said it as well.
I know people who swear that its not the same band that sang those two songs and then put out “come dancing” 20 years later … they just ant wrap their head around it
I feel like the Jefferson Airplane to Jefferson Starship to Starship should be mentioned.
Though I don’t know if the band that wrote"Somebody to Love" and “Whiten Rabbit” is considered to be the same band that wrote “We Built This City” and “Nothing’s Gonna Stop Us Now”.
Yes, that was a really weird direction to take. 
The Beach Boys’ early sound has been often copied and pastiched, but they moved on past it.
Yeah[quote=“Thudlow_Boink, post:18, topic:921540, full:true”]
The Beach Boys’ early sound has been often copied and pastiched, but they moved on past it.
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Yeah, the Beatles’ “Back in the USSR” was a parody of a Beach Boys sound that no longer existed in 1968.
Van Halen. While they always had a streak of “pop” in them, Sammy Hagar’s addition flipped the formula from mostly heavy rock with some pop, to mostly pop with just a token heavy song or two on each album.