It was Apple's version of DOS (also called ProDOS... not to be mistaken for MS-DOS,
DOS just stands for
Disk
Operating
System). If you need an OS for an Apple II, you can find some of the stuff you need
here (including version 3.2 of the System Disk).
What set the Macintosh apart from the Apple II was things like a super fast processor (Motorola's 68000 running at 8 MHz), tons of RAM (128k, twice what the average home PC had) and much of the important aspects of the operating environment stored on ROM within the computer (this was how you could have the GUI based OS, some apps and files all on a 400k floppy).
The first (and I think only) Apple II to have a GUI based OS was the Apple IIGS... if you have one of those you'll need to go
here for it's software (System 6.0.1). The interface is
Mac-like, but it still isn't a Mac (nothing else is

).