Battlezone and Battlezone II are not the only games under the Battlezone name; Activision licensed their name from Atari, who have created several games under it both before and since.
Battlezone (Arcade) =
The original game of its name, Battlezone was a vector-based wireframe tank game in which players were required to destroy other tanks and flying saucers. It became notable as one of the first games to use a 3D perspective, and its realism was such that a version of it was commissioned by the United States military to train soldiers to use Bradley tanks. It was this version of Battlezone which provided the original inspiration for Activision's series, with the flying saucers analogous to the Furies.
Battlezone (PSP)
In 2006, Atari rebooted Battlezone with a arena-deathmatch-based PSP game. It has some design similarities to the Battlezone series, such as hovertanks, but is completely unrelated.
Battlezone (XBLA)
In 2008 Atari again rebooted the game, this time commissioning Stainless Games to produce a remake of the original. It features both a vector version similar to the original and a 3D rendered version.