There are two types of HDD generally in use, the `old` ATA type click here and newer SATA type click here or click here for a composite rundown.
Most newer computers will support SATA HDDs internally but you would need to check with your manual to make certain.
For external HDDs, most connect via the USB ports on the PC (some are firewire) and the enclosure used for the drive will have the necessary hardware for the type of drive it uses. This means that for an External HDD it really doesn`t matter which type you get as it will connect and should function via the USB. However you may find that External SATA HDDs are a bit more expensive than the more usual ATA units.