PCI IDE Controller
IDE is a keyword points to the semi-conductors on the mother-board that controls ATA Drives(like ATA Hard-Disks). ATA (AT-Attachment) is the interface of this drives. IDE also can be an IDE card connected to PCI.
ATAPI is an extension to ATA. ATAPI (ATA Packet Interface) adds the support of Drives wich uses SCSI Command-Set (like ODDs (Optical Disk Drives .e.g CD-ROMs, DVD-ROMs), Tape Drives, and ZIP Drives).