The title probably sounds a bit confusing so let me explain through example.
Alter Bridge
Alter Bridge is a rock band formed up of most of the members of Creed. The biggest difference is that Creed's infamous lead vocalist, Scott Stapp, is NOT in Alter Bridge, instead vocals are provided by Myles Kennedy. The general consensus is that Alter Bridge is a huge improvement over Creed, leading many to realize Stapp was the weakest link in Creed, and that without him the other members (plus Kennedy) are able to really shine and put out music that's actually well liked by many.
Wovenwar
Similar to Alter Bridge, most of Wovenwar is made up of members of a previous band minus the lead vocalist of said previous band. In this case As I Lay Dying, a metalcore band that was pretty big back in the 00s. AILD's vocalist Tim Lambesis was arrested in 2013 because he tried to hire a hitman to murder his wife (the "hitman" he contacted turned out to be an undercover cop), and the rest of the band decided it was better to just abandon the As I Lay Dying name since they knew the name would now be connected to Lambesis' infamy. They hired Shane Bay of Oh, Sleeper to be their new vocalist and reformed under the new name Wovenwar.