What is the difference between BIOS and firmware?

As others already stated, BIOS is the specific name for the (motherboard) firmware in older PCs. New computers these days have a technically somewhat different kind of firmware which is called either EFI or UEFI.

Please note that any computer will contain, besides the BIOS (or EFI or UEFI), also other firmware. Network cards, video cards, RAID controllers, hard drives, flash drives, SSDs, sound cards, just to name a few examples, can all have firmware embedded inside the device.

Weirdly enough, the firmware of a video card is often called the video BIOS. This is technically incorrect. BIOS is appropriate only for the startup firmware of the motherboard itself.

So, BIOS is firmware for computers.

As you continue to read about computers, you will get the picture of BIOS, UEFI, EFI and so on.

The BIOS an acronym for Basic Input/Output System and also known as the System BIOS, ROM BIOS or PC BIOS) is a type of firmware used during the booting process (power-on startup) on IBM PC compatible computers.The BIOS firmware is built into PCs, and it is the first software they run when powered on. The name itself originates from the Basic Input/Output System used in the CP/M operating system in 1975.

Firmware is the combination of persistent memory and program code and data stored in it.Typical examples of devices containing firmware are embedded systems (such as traffic lights, consumer appliances, and digital watches), computers, computer peripherals, mobile phones, and digital cameras. The firmware contained in these devices provides the control program for the device.

Firmware is a generic name for all the software that is embedded on non-volatile memory. BIOS is stored in ROM, so it is firmware.