BIOS is the short form to Basic Input Output System and it refers to a set of instructions that are critical for the functioning of the system.
These instructions include information about the components connected to the motherboard, like the hard disk, RAM, and the configuration of the many onboard subsystems.
CMOS is the short form to Complementary Metal Oxide Semiconductor and it refers to the chip on which the BIOS instructions are stored.
CMOS is the name of the technology behind the chip that stores the BIOS.
Present-day CMOS is technically called EEPROM for Electronically Erasable Programmable Read-only Memory.
These can be rewritten to, and this allows the BIOS instructions of a motherboard to be updated when required.