BIOS
Basic Input-Output System: software program, usually written in assembly language, which starts a computer when power is turned on or when computer is reset. I will do tasks such as POST (Power-On Self-Test), which initializes and identifies system devices such as the video display card, keyboard and mouse, hard disk drive, optical disc drive and other hardware. The BIOS then locates boot loader software held on a device (designated as a 'boot device'), such as a hard disk or a CD/DVD, and loads and executes that software, giving it control of the PC. BIOS software is stored on a non-volatile ROM (Read-ONly memory) chip (the "BIOS CHIP") on the motherboard. It has a menu type user interface where some settings can be changed. These settings are stored in....
CMOS
Historically the first PCs in the 1980s used special NVRAM (Non-Volatile RAM) made with CMOS (Complementary Metal Oxide Semiconductor) technology to store BIOS settings. It needed a battery to retain its contents when the power was off. This term is still widely used but nowadays the job is often done by EEPROM or flash memory. The remaining usage for the battery is then to keep the real-time clock going. Typical NVRAM capacity is 512 bytes. The CMOS RAM and the real-time clock are usually part of the motherboard chipset on modern motherboards.
So the BIOS is software ("firmware") and the CMOS is the memory it uses. They are not the same thing but many non-technical people use the words interchangeably.