the definitions for you:
IDE: A type of disk-drive interface in which the controller electronics reside on the drive itself, which eliminates the need for a separate adapter card. The IDE interface is compatible with the controller that IBM used in the PC/AT computer, but offers advantages such as look-ahead caching
EIDE: Enhanced Integrated Digital Electronics. The current standard for hard drives. Replaces the original IDE specification. The controller is built into the drive, and does not require an accessory card on the bus
ATA (AT Attachment): A disk drive interface standard for integrating drive controllers directly on disk drives. The ANSI X3T10 working group developed this standard. ATA includes the ATA-1, ATA-2, Fast ATA, and Parallel ATA standards
ATAPI: Short for AT Attachment Packet Interface, an extension to EIDE (also called ATA-2) that enables the interface to support CD-ROM players and tape drives.
Serial ATA: Often abbreviated SATA or S-ATA, an evolution of the Parallel ATA physical storage interface. Serial ATA is a serial link -- a single cable with a minimum of four wires creates a point-to-point connection between devices. Transfer rates for Serial ATA begin at 150MBps. One of the main design advantages of Serial ATA is that the thinner serial cables facilitate more efficient airflow inside a form factor and also allow for smaller chassis designs. In contrast, IDE cables used in parallel ATA systems are bulkier than Serial ATA cables and can only extend to 40cm long, while Serial ATA cables can extend up to one meter
With that said... This is the simple of it.
In the old days we had IDE which was great, but slow. Then came EIDE and extends to today. The ATA standard came out to provide enhancments to the drive technology so things got faster. ATAPI has been around for a while so we have CDroms and such. PATA (EIDE ATA) is the standard drive spec for all desktop and laptop drives. SATA is an up and coming technology that offers many enhancments on an old specification. Not only is it faster, but it's a simpler technology, with smaller cables to boot. SATA works on a dedicated connection to each drive and can support higher data transfer and sustained speeds than ATA. SATA is a HDD technology, that as far as I know is not meant for the CD world, so we won't be seeing IDE free system for a while.
Hope that helps.