There is a very slight difference. For one thing, you would say "a skillful performance." I don't believe you would hear "a skilled performance." When "skilled" is applied to a person ("a skilled carpenter"), it means that the person has had training and experience and that they are good at what they do. A "skillful" person implies training and experience, but also implies talent and ingenuity. "A skillful liar." This is not a clear line between the two. You will see a lot of overlap in use. If you violated the above guidelines about describing a person, I doubt that anyone would notice.

Both are correct.