is this person considered same as jew or whats the difference ?

ב"ה Shalom Giyur Lechumra is done when the assumption is that perhaps the person is already a Jew, but since some doubts have arisen, a Jewish court= Bet Din will decide if giyur has be done to remove any doubts about the person's Jewishness. A convert is a person, who with no doubt has come from a non-Jewish background, and has done the conversion process and become a convert. Ultimately, they are the same, except for the fact that perhaps the person who did Giyur Lechumra was already Jewish. All the best