Mainframes are large centralized computers. At one time they provided the bulk of business computing through time sharing . When mainframes were in widespread use, there was also a class of computers known as minicomputers which were smaller, less expensive versions of mainframes for businesses that couldn't afford true mainframes. Servers are also sometimes used as mainframe replacements. Desktop operating systems are used for personal computers .
Workstations are more powerful versions of personal computers.
Handheld operating systems are much smaller and less capable than desktop operating systems, so that they can fit into the limited memory of handheld devices. Embedded systems are combinations of processors and special software that are inside of another device, such as the electronic ignition system on cars. There was competition in features of both the operating system and the underlying hardware. Eventually UNIX spread into the business community, and pushed aside almost all proprietary mainframe and minicomputer operating systems. Even IBM and DEC ended up offering their own versions of UNIX as well as their proprietary operating systems.