What type of OS is very fast and small, and is often embedded, or built into the circuitry of a device?

Real time operating system (RTOS)

Explanation:

Real time operating system is an operating system software which is used for the real-time applications that processes the data as soon as the input comes to the system.

It is very fast because it processes the data without any buffer delays.

In RTOS the scheduler provides a deterministic time which is predicted for the execution pattern. In a real-time operation the system must respond to each sequence of execution within a certain time frame which is the deadline for the operation so that the next inline process can be executed. Hence it is used in embedded systems and circuitry devices.