Bally first made the Astrocade, but it was called the Bally Professional Arcade.Bally's sales were bad,so they sold the system in 1978. The Bally professional Aracade was re-released by an unknown company called Astrovision as the "Bally Computer System." Then, in a move that must have been an attempt to start over without the Professional Arcade's failure looming overhead, in 1982 it was renamed simply as "Astrocade." Perhaps the most significant contribution this system had to the industry, was that its programming abilities would inspire many of the current generation of video game producers. The Astrocade was actually just the Bally home entertainment system after Bally sold it to another company (forget who, astro someone). Search the net, you're likely to turn up info.
I have a site dedicated to this system. Check it out (there are NO others at all that are Astrocade exclusive as far as I know): www.ballyalley.com
The Bally Astrocade is exactly the same as the Bally Home Arcade. There is no difference in rarity, games, or control.
I came across one of these at a garage sale for about $5.00. It came with a few joysticks and some loose cartridges. The games are encased plastic, they look very similair to a cassette tape case, but where the tape would be is the cartride contacts. The joysticks are very unique, they are a combination of 8 way joystick with trigger and the joystick also doubles as a paddle. I picked up another unit several months later at a garage sale, it functions but makes noise and turns itself off after a few minutes. The second unit included the basic language cartridge along with the manual for basic and several more games. I now have 2 units, 4 joysticks and a dozen games. Graphics wise its very similair to the Atari 2600 but its no ColecoVision. This was a unique unit that was overlooked when it was released, definately a collectors item and can even be found on e-bay for a reasonable price.