Grateful means thankful. Gratified means satisfied or pleased—or, often, pleased to receive something one has worked for or long desired. Gratification doesn’t necessarily involve gratitude; for instance, one might be gratified to see positive effects of one’s hard work, or a victim of crime might be gratified to see the criminal sentenced to prison.
The two words can come close together in meaning, such as when one is grateful to have received something gratifying. In the third example below, for instance, the speaker is thankful that he has a girlfriend but is presumably also pleased, hence gratified, by what she does for him.
She says that overcoming such serious illnesses has made her grateful for the tiny things in life. [Irish Independent]
John von Neumann would have felt reassured and gratified, I believe, by the choices his progeny and his progeny’s progeny have made. [The Legacy of John Von Neumann]
I wouldn’t have cared if my girlfriend was a Jaguar-driving Cyclops with a beard—I’d have been grateful just to have someone to make out with. [Looking for Alaska, John Green]
The Prime Minister’s speech on Europe was a gamble and he must be gratified at the mostly supportive response. [Evening Standard]
He mentioned several times about how grateful he was to the Rangers for the security they have given his family. [MLB.com]
HarperCollins declined to give further details of the settlement, but said in a statement that it was “gratified.” [Daily Beast]