External Hard Drivesare used for backing up, and can be used to transport data (where flash drives are not large enough). They come in two main types - 2.5" size (very portable, but expensive for the higher capacities), and 3.5" size (less portable, but large capacities reasonably cheap).
2.5" PATA/Parallel ATA IDE Notebook Drivesare what most laptops use (more than 3-4 years old). They are also often used with external enclosures to create relatively small backup storage solutions (compared to standard 3.5" drives). Parallel ATA or PATA connections are used in almost all laptops over about 4 years old, other than super-small ones (which sometimes use 1.8" drives). Younger models use the Serial ATA or SATA drives (see below).
2.5" SATA/Serial ATA Notebook Drives are used by the latest laptops (under 3-4 years old). Connections are faster, and drive connectors are more simple than the PATA drives. It is not possible to use a SATA drive where a PATA drive is required, the two are not easily interchangeable.
3.5" PATA/Parallel ATA IDE Desktop Drives are the standard drives used in almost all desktop computers. The connectors are the most common ones used, which are also used by CD-ROM drives etc. Most computer cases/motherboards/power supplies will not need additional adapters or connectors for these drives, as even the latest computers generally have at least one IDE port available (previous standard was 2 ports (up to 4 IDE drives). The cables are large and fairly bulky.
3.5" SATA/Serial ATA Desktop Drivesare the latest type of hard drive providing speeds up to 150Mb/s, used in the newer desktop computers (less than 3 years old). The connections are quite specific, and the motherboard must support such drives - which most late model motherboards will.