Yes—the operating system is running. Mostly it is managing the user interface, waiting for some input to tell it what to do.
The operating system is a complex program that keeps the hardware and software components of a computer system coordinated and functioning. It is like the owner of a small shop, who keeps everything in order by attending to customers, handling supplier deliveries, stocking the shelves, doing the bookkeeping, and so on. The shopkeeper must promptly attend to tasks as they arise. Without the shopkeeper the shop could not function.
Most computer systems can potentially run any of several operating systems. For example, most Pentium-based computers can run either Linux or a Windows operating systems. Usually only one operating system is installed on a computer system, although some computers have several. In any case, only one operating system at a time can be in control of the computer system. The computer user makes a choice when the computer is turned on, and that operating system remains in control until the computer is turned off.
(Review:) What component of a computer system holds the operating system when the computer is not running?