Atari Basketball (arcade) oddly enough came out after the Atari 2600 version, which is rare because generally it's the opposite, Arcade games are often adapted to home consoles or computers. Yet the relationship between these two versions is obvious. It is therefore clearly the same project.
One can legitimately ask whether in fact the arcade project did not start first but took longer to be developed. We would have to ask the question to the developers: Chris Downend for the arcade version and Alan Miller for the Atari 2600.
The arcade game is one of the first (with Atari Football) to use a trackball, two in fact for paced two player action.
As described for the Atari 2600 version, Basketball was the first "real" basketball videogame. There has been pong variations before, but this basketball game from Atari was the first to use human shaped players and a pseudo-3D playfield, along with real basketball features like dribbling, blocking, stealing and adjustable shots.