Skilled and skillful cover pretty much the same semantic domain; but they are used differently.
Skilled is in origin a past participle, and retains something of that verbal sense: it is used of a person who has acquired skills (a skilled musician, surgeon, cabinetmaker) , or a calling which requires that its practitioners acquire skills (the skilled trades, the skilled professions). There is a tendency (no more) to use it where physical rather than intellectual skills are in play: a barrister is a little more likely than a solicitor to be described as skilled, because his skills lie in performance before an audience.
Skillful may be used similarly; but it may also be used of the works, as skilled may not. We do not speak of performances or surgeries as being skilled but as skillful: these demonstrate or exhibit the skills which the performers or surgeons possess and which are exhibited in the works. For some reason we do not often speak of physical objects as being either skillful or skilled; but we do speak of them as being skilfully made, not skilledly made.