Late as ever... since its clear as mud, maybe I can clarify more?? Maybe not:
Driver. This is the intruction manual for your OS. Without the driver, the OS has no idea on how to operate s specific piece of hardware. You can see why driver updates are important - a new section may be added to the "manual" so that the OS can work better with the device.
Firmware. This is the on-board instruction manual for the device. Essentially it is also an instruction manual for your BIOS and any testing equipment. Without this, your PC wouldn't even know what the device is!
So you do need both of course.
The idea of Firmware may become clearer if you imagine that your Digital TV receiver, mobile phone, microwave, and lots of other things have it. Of course, they don't require "drivers", because there is no "3rd party" manipulating the device.