Bally BASIC is the original cart that required the 300 baud interface to save tapes.
It has only one array. Can access the calculator functions through the $ command and must use the &(n) sound ports directly.
Astro BASIC is the later cart with the 2000 baud interface built in.
It has 2 arrays, no $ functions and the two letter 'Music Processor Commands'. Which require you to set NT=-1 for the older style &(n) sound commands to work properly.
Most type in programs for Bally BASIC will work fine in Astro BASIC. More if you remember to set NT=-1 if it is using the &(n) sound commands.
Tapes of course, have to be converted, as they are not only two different speeds, but Bally BASIC dose an ascii dump to tape and Astro BASIC does a complete RAM dump to tape.
The RAM dump save can give a nice loading screen.