Desktop and laptop PCs have virtually the same backup requirements. Almost anything you can connect to a Desktop can be connected to a Laptop. The term Desktop as used for external drives, refers to the drives' form factors: bigger ones are for desktop (non-portable) use, while Portables are for on the go use. (Although portables also function perfectly well when used at home.)
For backup purposes, desktop drives are slightly more reliable, but that difference is getting less and less as time goes by.