The word “graceful” is normally used to refer to a person’s movement; the individual moves in a way that is attractive to watch.
*The young dancer moved gracefully across the stage. *For someone who was terribly overweight, Eshwar was surprisingly graceful.
The word can also be used to talk about an object which is pleasing to looking at.
*He had a graceful little cottage in the countryside.
“Gracious”, on the other hand, refers to people who are pleasant and polite. It is considered formal.
*Janaki is the gracious lady you met last week.