Once disembodied, an incarnate Maia becomes a discarnate spirit (just like Elves and Men). But notice how Saruman's end played out- that spirit actually was visible, a shadowy form rising from the body, which looked almost pleadingly into the West before a great wind blew it away (that was Manwe saying "You're fired!") Exactly the same as Sauron, except Sauron's shadow-spirit was much, much bigger.
But Radagast certainly never became a villain and didn't earn "spirit of malice gnawing itself forever in the dark" status, so we would have to assume that Radagast simply defaulted to base-Maia status, an incorporeal being with the ability to don or doff physical forms at will.
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The entire plot of The Lord of the Rings could be said to turn on what Sauron didn’t know, and when he didn’t know it.
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