Here are variants of each interface, and this article will not do justice to the different types of ATA, SATA and SCSI interfaces. Thus, it will only highlight the more common interfaces as used by the home user.
SATA is basically an advancement of ATA.
ATA is a common interface used in many personal computers before the emergence of SATA. It is the least expensive of the interfaces.
SCSI is commonly used in servers, and more in industrial applications than home uses.