What is the difference between ASPI, ASAPI and Native drivers?

EAC communicates directly with the CD-ROM drives. For this EAC make use of several interfaces which do the low level work. You can choose the interface by your own in the EAC options (depending which interfaces are installed in your computer).
ASPI is from Adaptec, it comes preinstalled in Win95/98. In all other Windows it needs to be installed, but in these OS the installer tests if any Adaptec hardware is in your computer. Nevertheless you can try to install it, download for Windows 95 only and all other windows versions.
VOB produced a replacement called ASAPI. It is freely available from here.
In WinNT/2000/XP EAC is able to use a native interface in that OS. This is still buggy and only recommended when you don’t want to install 3rd party software. Nevertheless, this will only work if you are logged in with admin rights. If you encounter problems, it is strongly recommended to download ASAPI and to change the interface to that.