"Super Luigi Galaxy" is not a game you can buy at the store. But, you can buy Super Mario Galaxy and unlock Luigi. To unlock Luigi on Super Mario Galaxy, you need to get all 120 stars. Then, you can play Super Mario Galaxy as Luigi.
Yes, Luigi is Mario's twin brother, in fact. Luigi is the "brother" in "Super Mario Brothers". They are called the "Super Mario Brothers" because Mario is the older twin, more popular than Luigi, and was introduced 2 years before Luigi in 1981.