The terms probably have some formal definitions that aren't commonly adhered to. The general point is that CIA spooks don't work out of CIA HQ in Langley. People who drive in and out of that compound are known to be CIA employees, no way or reason to keep that fact covert.
They can and do if they are reassigned back to headquarters on a domestic assignment. Thousands of people work there and unless a specific individual is being tracked by a hostile power inside the US, it would be difficult to sort out who does what.
There are many levels and kinds of cover. Many CIA personnel are declared to host governments when they are assigned abroad and attached to the Embassy. It facilitates host country protection and working with intelligence officials abroad.
Pfame's usefullness to the Agency as a covert operative was severely damaged when her husband declared in his Op-Ed piece that he was on a mission for the CIA to Niger. His association with the CIA and his new high public profile would make it difficult for his wife to be assigned overseas with her family. She was now Mrs. Wilson, wife of CIA operative, Joseph Wilson.