From https://en.wikipedia.org/wiki/Firmware

History and etymology

Ascher Opler coined the term firmware in a 1967 Datamation article,[2][failed verification] as an intermediary term between "hardware" and "software". In this article, Opler was referring to a new kind of computer program that had a different practical and psychological purpose from traditional programs from the user's perspective.

As computers began to increase in complexity, it became clear that various programs needed to first be initiated and run to provide a consistent environment necessary for running more complex programs at the user's discretion. This required programming the computer to run those programs automatically. Furthermore, as companies, universities, and marketers wanted to sell computers to laypeople with little technical knowledge, greater automation became necessary to allow a lay-user to easily run programs for practical purposes. This gave rise to a kind of software that a user would not consciously run, and it led to software that a lay user wouldn't even know about.[3]

Originally, it meant the contents of a writable control store (a small specialized high-speed memory), containing microcode that defined and implemented the computer's instruction set, and that could be reloaded to specialize or modify the instructions that the central processing unit (CPU) could execute. As originally used, firmware contrasted with hardware (the CPU itself) and software (normal instructions executing on a CPU). It was not composed of CPU machine instructions, but of lower-level microcode involved in the implementation of machine instructions. It existed on the boundary between hardware and software; thus the name firmware. Over time, popular usage extended the word firmware to denote any computer program that is tightly linked to hardware, including BIOS on PCs, boot firmware on smartphones, computer peripherals, or the control systems on simple consumer electronic devices such as microwave ovens, remote controls.

But firmware doesn't have to be from the firm that manufacturers said chipset. Third party firmware is a common thing.