The smaller S/360 models used Basic Operating System/360 (BOS/360), Tape Operating System (TOS/360), or Disk Operating System/360 (DOS/360, which evolved into DOS/VS, DOS/VSE, VSE/AF, VSE/SP, VSE/ESA, and then z/VSE).
The larger S/360 models used Operating System/360 (OS/360): Primary Control Program (PCP), Multiprogramming with a Fixed number of Tasks (MFT), which evolved into OS/VS1, and Multiprogramming with a Variable number of Tasks (MVT), which evolved into MVS. MVT took a long time to develop into a usable system, and the less ambitious MFT was widely used. PCP was used on intermediate machines; the final releases of OS/360 included only MFT and MVT.
When it announced the S/360-67 in August 1965, IBM also announced TSS/360 (Time-Sharing System) for delivery at the same time as the 67. TSS/360, a response to Multics, was an ambitious project that included many advanced features. It never worked properly, was delayed, canceled, reinstated, and finally canceled again in 1971. It was replaced by CP-67, MTS (Michigan Terminal System), TSO (Time Sharing Option for OS/360), or one of several other time-sharingsystems.
CP-67, the original virtual machine system, was also known as CP/CMS. CP/67 was developed outside the IBM mainstream at IBM's Cambridge Scientific Center, in cooperation with MIT researchers. CP/CMS eventually won wide acceptance, and led to the development of VM/370 (aka VM/CMS) and today's z/VM.
The S/360 Model 20 offered a simplified and rarely used tape-based system called TPS (Tape Processing System), and also DPS (Disk Processing System) that provided support for the 2311 disk drive. TPS could run on a machine with 8K of memory, and DPS required 12 K, which was pretty hefty for a Model 20. Many customers ran quite happily with 4 K and CPS (Card Processing System).
With TPS and DOS, the card reader was used (a) to define the stack of jobs to be run (Job Control Language), and (b) to feed in transaction data, like customer payments. But the operating system was held on tape or disk, and results (master files!) could also be stored on the tapes or hard drives. Stacked job processing became an exciting possibility for the small but adventurous computer user.
A little known and little used suite of 80 column punched-card utility programs known as Basic Programming Support (BPS) (jocularly: Barely Programming Support) was available for the S/360-30. It was a precursor of TOS on the Model 30.