Having both seems a bit redundant, and the latter is used more, as well as being more meaningful (IMO).
A Desktop is a specific type of interface in addition to a type of computer. [desktop-application] fits applications designed for a desktop computer, but not questions about desktop style interfaces. We even have at least one question about these sort of interfaces.
The most common one is probably the Windows Desktop:
Note that desktop interfaces aren't always [desktop-applicaitons]. The iPhone Homescreen is also a desktop:
IMO, [Desktop] should have it's tag wiki rewritten and made to focus specifically on these desktop interfaces rather than be a synonym of desktop-application.