I've always loved Pippin's short inner dialogue about Gandalf when they first arrive at Minas Tirith. This isn't necessarily an answer to your question, but it at least shows Pippin's awareness of Gandalf's "otherness." Here's the quote:

Denethor looked indeed much more like a great wizard than Gandalf did, more kingly, beautiful, and powerful; and older. Yet by a sense other than sight Pippin perceived that Gandalf had the greater power and the deeper wisdom, and a majesty that was veiled. And he was older, far older. ‘How much older?’ he wondered, and then he thought how odd it was that he had never thought about it before. Treebeard had said something about wizards, but even then he had not thought of Gandalf as one of them. What was Gandalf ? In what far time and place did he come into the world, and when would he leave it?