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.
Carmageddon is a notorious vehicular racing/combat game developed by Stainless Software and published by Sales Curve Interactive for MS-DOS PCs in 1997.
It was originally meant to be a game based on the Mad Max series of films. When that didn’t happen the developers then bought the license to the infamous Roger Corman/Paul Bartel film Death Race 2000, but they later decided to drop it and create their own IP, eventually coming up with the title “Carmageddon“.