Is the difference of two context-free languages still context-free?
The complement of a context-free language $L$ is not necessarily context-free, but it is the difference between two context-free languages ($\Sigma^* - L$). (Here $\Sigma$ is the alphabet of $L$.)

See, for example, Is the complement of { ww | ... } context-free? for an example of a context-free language whose complement is not context-free.