linking the swain family of nantucket to the swain family of Gloucester county NJ

I believe my 3g grandfather John Swain of Gloucester county NJ is the same John Swain born on Nantucket june 26 1817. His parents where Franklin Swain and Anna Cathcart. Does anyone have any information to prove or disprove this? I am new on here and don't want to fill my tree until this can somehow be confirmed. I have just sent my DNA in, but not sure if that will give a direct answer.