This is not accurate.
Yeah, I noted that, but wasn’t going to pursue. There are a few posts that aren’t quite right (heck look at mine regarding New Order)…
I don’t think this one has been mentioned, perhaps due the general good taste of this place: Alter Bridge is Creed with a different singer. And of course, that guy is now Slash’s singer.
Kevin O’donnell’s Quality Six is the exact same lineup as Andrew Bird’s Ball of Fire. Except for writing credits I think.
Please cite. Any info I can find suggests no connection (save genre) whatsoever.
Emerson, Lake & Powell and Emerson, Lake & Palmer replacing Palmer for Powell 
The short-lived ELPowell was followed by the even shorter-lived 3, which was Emerson, Lake & Palmer with Robert Berry replacing Greg Lake.
On a similar tip: Refugee was the Nice with Patrick Moraz replacing Keith Emerson.
Mallard was Captain Beefheart and His Magic Band without Captain Beefheart.
Perhaps I misunderstood the OP. I thought we were looking for the indescribable quality that one person brought to an act that all the soundalike or spinoff groups simply couldn’t recapture.
I stand corrected! I could have sworn Jerry Harrison was in Tom Tom Club.
Nope, I was just looking for bands that had an identical lineup to another band except for one band member.
However, what I wasn’t very clear about was that I was looking for bands with different names. While technically correct, CSN/CSNY and ELP/ELP aren’t exactly the kinds of examples I was looking for.
The Other Ones is basically the Grateful Dead without Jerry Garcia. They later changed their name to “The Dead.”
The Beatles are a couple of Quarrymen lineups without Ken Brown / Stuart Sutcliffe plus Ringo
ABWH is Yes minus Chris Squire + Tony Levin
No post-Garcia lineup has missed ‘replacing’ Garcia with fewer than two other people.
One too many negatives in that sentence, methinks.
No one ‘replaced’ Jerry. 
The Mitchell Trio was the Chad Mitchell Trio with John Denver instead of Chad Mitchell.
It’s a bit complicated, but for practical purposes, the Foo Fighters are Nirvana without Kurt Cobain.