Does Saruman lose his ability to use magic when his staff is broken?

[Ghanberryghan]

In The Lord of the Rings I had a hard time distinguishing between 'magic' and 'power'. I normally thought that Saruman didn't because he still had his voice which was more "powerful than rhetoric" - implying that his voice is what gave strength to his speech rather than his choic of words.

And when Gandalf breaks Saruman's staff he later goes on to say: "He has power still whilst in Orthanc, I think, to resist the nazgul. He may try to trap it, or slay the steed it rides upon." Was he implying Saruman can still use magic?
But at the same time, when in the Shire, Frodo tells the other hobbits that Saruman has lost all power save his voice.