ATA is the AT Attachment interface, one of two major standards for connecting storage media devices like hard drives to personal computers (PCs). The opposing standard is SCSI.
PATA is the Parallel ATA specification. Mostly incorrectly referred to as IDE (Integrated Device Electronics) by a lot of vendors. SATA is the Serial ATA specification.
ATAPI is an extension on the ATA standard for optical media, like CD, DVD, Blu-Ray.