Firmware is the program that lives inside the device itself - the router, SSD, monitor, printer or the PC's own UEFI/BIOS - while a driver lives in Windows and only talks to the device. The two get mixed up constantly, and the fix for a misbehaving device is much more often the driver than the firmware. This guide sorts out which one you actually need, and how to update firmware without hurting anything.
Quick answer
First check whether you need firmware at all: most device problems are driver problems, and drivers update safely from Windows Update or the maker's site. Real firmware updates come ONLY from the device maker - through Windows Update's optional updates, the maker's own updater app, or a download for your exact model. Golden rule: never interrupt a firmware update - no unplugging, no shutdown, laptop on charger.
It boots the device before Windows even sees it. UEFI/BIOS is the PC's own firmware; SSDs, routers, monitors and printers all carry their own.
Drivers are installed and updated on the PC and never touch the device's insides. Nine problems out of ten that people google end at the driver.
Security holes, compatibility with new hardware, stability bugs in the device itself - that is firmware territory. Speed and features inside Windows - driver territory.
A bad driver install is undoable. An interrupted firmware update can leave the device unbootable - which is why the safety rules below exist.
Usually not - "not working in Windows" is a driver-layer symptom in the vast majority of cases. Fix the driver first (it is quick and reversible); reach for firmware only when the maker's notes say your specific issue is a firmware fix.
Done from the official source, on stable power, without interruption - it is routine. The real risks are wrong-model files from third-party sites and pulled power mid-update. Follow the safety rules above and the danger drops to near zero.
Some do - Windows Update ships vendor firmware for many laptops and SSDs, routers often self-update, printers can update from their panel. Others wait for you in the maker's app. Checking the maker's tool once in a while covers the gap.