[William Cloud Hicklin]

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.