There are two physical sizes of disks - 3.5" (that go in desktops) and 2.5" (that go in laptops).
3.5" desktop drives require a mains supply so a desktop external hard drive can only be used near a mains socket.
2.5" laptop hard drives can (normally) get all their power from the USB socket so can be used "on the go (portable).
Desktop drives can usualy hold more data (they go up to 2Tb) whereas laptop drives are smaller (they go up to 1Tb).
You generally pay more for a "portable" drive than a "desktop" drive (for the same gigabyte size)