Gwaihir = Lord of the Eagles?

I had long thought that the "Lord of the Eagles" mentioned in the Hobbit was the same as Gwaihir the Windlord in LotR. However, when I got The Annotated Hobbit last summer, it changed my mind.

"Many Tolkien commentators have been tempted to equate the Lord of the Eagles in The Hobbit with Gwaihir, the Windlord, the eagle who rescues Gandalf in The Lord of the Rings. The evidence, however, is inconclusive, and one is left with the thought that if Tolkien had intended them to be the same, he would most likely have stated it."

I can't help agreeing with annotator Douglas Anderson that Tolkien would probably have mentioned it. For example, the Elvenking of the Hobbit is clearly stated to be the same person as Thranduil, but no such claim is made about Gwaihir/LotE.

And yet Robert Foster's Guide to Middle-earth states that the two are the same.

Thoughts?