No, the Greek words are not the same - but both are based on the root word for “grace”.
The Greek in Luke 1:28 is “kecharitomene” (a single word) and is used by the angel instead of her name (Mary). I know this has been discussed one of the forums before. Try a forum search on kecharitomene - or you can do a google search on the word.
The Greek in John 1:14 uses two words - one for “full” and one for “grace”.
Nita