Yes, they mean the same thing, but I think the main difference is in the level of formality. For example: "Have you been here awhile?" [which seems very informal], compared to: "Have you been here for a while?" [which seems a more formal]. :)

I'd also add that 'for a while is more flexible because you can use it at the beginning of the sentence, whereas 'awhile' is generally only used after the subject and verb E.g. For a while, we wandered OR we wandered for a while. Sit here awhile, and sing to me, but NOT awhile sit here and sing to me.

yes they are the same :)