I’ve always regarded graceful as meaning elegance or smoothness of style, physical or otherwise; “he gave in gracefully”, for example. Being gracious is being nice or polite.
You can gracefully slice someone’s head off, but you can’t graciously do so.
“Gracious” refers to one’s behaviour with regard other people; “graceful” refers to one’s behaviour with regard one’s self. You can certaily be a gracious klutz or a graceful asshole.