Firmware is software which is stored in non-volatile (or perhaps even read-only) memory. Because it is stored in such memory, firmware is available when the machine is turned on. The machine may almost immediately begin executing firmware when it is turned on, or some small boot program (itself firmware) can pull the bigger firmware from some electronic storage such as flash and put it into RAM, and then execute it.
Firmware can be a “full blown” operating system. For example, Tomato is a Linux-based firmware for wireless routers:
http://www.polarcloud.com/tomato
We can log into Tomato via ssh, and get a Linux prompt. So it is an advanced operating system, and it is firmware. But if the router had a hard disk in it, and if the same OS had to be loaded from that disk at startup, it could no longer be legitimately called firmware. Firmware has to be in electronic storage that is accessible to the processor immediately on power up, like flash memory or EPROM chips.
Firmware and software are the same thing; the only distinction is in how it’s stored. Software is typically stored on a mass-storage device (e.g., disk drive) and loaded into volatile memory (e.g., DRAM) before being executed. It’s easy to change software, by simply replacing the file containing it with a different one.
Firmware is typically stored in nonvolatile memory (e.g., FLASH) connected more-or-less directly to the CPU. It’s harder to modify (hence the “firm”) and it may or may not be transferred to a different memory for execution.
Firmware is the software that runs on the device. A driver is the software that tells your operating system how to communicate with the device. Not all devices have firmware–only devices with some level of intelligence.
The word “operating system” simply refers to a control program which has a certain degree of sophistication and completeness in managing the resources of the machine and providing reasonably high level services to programs: features like file systems, network protocols, memory and process management, high level access to devices, and perhaps some model of a user as well as security. Not all of these have to be present in an operating system. Usually the memory, process management and I/O are the key. If the control program allows other programs to execute, giving those programs an identity through which they are associated with their own resources, and if it provides services to them for managing the processor and memory, and doing I/O, we may call that control program an operating system.
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