Firmware is a kind of Software
A block of computer instructions, no matter how permanent and malleable they are, is Software.
Several devices are strictly connected with a portion of software. In these cases the hardware cannot run other software and that software only run on that specific hardware. We call this Firmware. And it’s still Software.
Other types of Software are Apps, Operative Systems, Videogames, Web Application Servers.
In electronic systems and computing, firmware[a] is a type of software that provides control, monitoring and data manipulation of engineered products and systems.
Firmware is a type of Software usually strictly connected with a device. Usually it doesn’t change during the lifetime of the device unless some update or bug fixing is required.
Wikipedia: Back in 2008, the second iteration of what we today know as iOS (the iPhone and iPad Operative System) was called iPhone OS Firmware 2.0. It was a Firmware (by definition) and definitely it was a Software.
Computer software, or simply software, is that part of a computer system that consists of encoded information or computer instructions, in contrast to the physical hardware from which the system is built.