Carmageddon: Max Damage is an updated version of Carmageddon: Reincarnation*, which was originally funded by a Kickstarter campaign and released in 2015. Max Damage was developed by (mostly) the same team who made the original Carmageddon and was first released in 2016, and is basically the same game as Carmageddon: Reincarnation but with better graphics and a few small changes to the game structure. The levels are mostly the same, although there are some new additions and tweaks here and there.
Carmageddon II: Carpocalypse Now is the 1998 sequel to the excellent Carmageddon. Although it was developed by the same team who made the first game (Stainless Software), and although it’s still fun to play to a certain degree, in my opinion it’s not a patch on the original.