Firmware is said to be “firm” in that it is difficult to change once it is programmed and loaded onto a hardware platform. Similar to software, the instructions that make up firmware are stored on a physical device, but the instructions are intended to be unchangeable once written.
firmware and software are both stored on hardware. The firmware is integrated at the hardware level, and can be a combination of mechanical and digital. This is probably where the confusion between software and firmware arises.
All firmware is software, but not all software is firmware.