The anime isn’t finished. I doubt they’ll ever make a second season. The manga, on the other hand, is finished. Out of 136 chapters of manga, the anime only makes it to chapter 33. A lot of things happen in the other 103 chapters that the anime never gets to, including things that happen to Tohru, Yuki and Kyo. Their relationships change; people learn secrets and meet other people. I’m not saying you have to read the manga, I’m saying you have to read the manga to get the full story. Whether you want the full story or not is a different matter.