User summary, some info gathered from Japanese and English wikipedia:
Bionic Commando (in Japan: Top Secret) is a series of arcade and home system games by Capcom. The original game was released for the arcades in March 1987 and was ported to several home systems in the West, like the ZX Spectrum, Commodore 64, Amstrad CPC, Amiga and Atari ST. The game is a 2D platform game where the player runs around on the screen killing enemies. The unique part of the game was that instead of jumping, the player could shoot out a bionic arm, a grappling hook, that could grab platforms above him and let him swing in his arm.
In 1988, Capcom produced a sequel for the Famicon called "Hitler's Resurrection" (Hitler no fukkatsu). This game was simply called "Bionic Commando" in the West, though it's not so much a port as a sequel to the original arcade game. It featured largely improved wire action, more story, other stages, and many things that separated it from the arcade version. This version was subsequently ported to the Game Boy, and remade for PS3 and Xbox 360 (see below).
In 1999, Nintendo of America released "Bionic Commando Elite Forces", a game for GameBoyColor, released only in the West. It featured, apart from the side-view 2D platform modes, also top-view vertical scrolling and sniper stages.
The year 2008 saw "Bionic Commando Rearmed", a remake of the Famicon/NES version, for Xbox Live arcade and Playstation network, and this spawned in 2009 a full game for Xbox360/PS3/Windows, called simply "Bionic Commando".
Thus there are several games, though different, that share the same name:
Bionic Commando (1987 original: arcade, in Japan "Top Secret", ported to many 8-bit and 16-bit home computers in the West)
Bionic Commando (1988, original: NES, in Japan "Hitler's Resurrection", ported 1992 to Game Boy and much later, 2008 to PS network/Xbox LA carrying the suffix "Rearmed")
Bionic Commando Elite Forces (1999, US GBC only)
Bionic Commando (2009, a direct sequel to the NES original/Rearmed)