They're not the same person but Rinoa did inheret her powers so she should've been able to take her on by herself. The cycle goes Ultimecia dies, Edea takes Ulteimecia's powers, Ultimecia gains control over Edea, years later. Edea's powers are given to Rinoa, gets possesed and unpossed and Squall and the party go to defeat Ultimecia which she dies and Edea takes her powers again at the orphanage.