EIDE is Enhanced IDE, which, to state the obvious, is an updated version of IDE. EIDE is still a pretty old standard. Your motherboard clearly isn't old if it supports ATA133, though.
So, to answer your question, IDE and EIDE are generally compatible. In fact, anytime you see IDE, it's probably just a lazy way of writing EIDE. Your motherboard, being a newer variety, will probably be able to support any IDE drive you can buy today, and it should even support the high performance features. Just steer away from Serial ATA (SATA) and SCSI drives.
This was first published in January 2004