Drivers are basically what let Windows and/or MacOS use the hardware attached to the computer. They are the translators, if you will. ASIO, WDM, etc... are just standards that drivers adhere to. If two different pieces of hardware are both WDM compliant, and you are using WDM compliant recording software, then it is most likely that the software could use either hardware device without any problems.
For a simplified example... I use Cakewalk Sonar for recording software. It understands how to "speak" WDM. I also have a Motu 828mkII firewire recording unit. It "speaks" Motu (more or less). So Motu wrote a driver that translates WDM commands and whatnot into commands that the 828 understands.
