No, oregano and basil are not the same thing. They are two very different herbs with very different flavor profiles.
Basil can be used as a substitute for oregano, however. Oregano is a herb that wasn’t often used in American recipes much before World War II, but has firmly become a staple on many dishes such as pizza. In contrast basil is a herb that can be used in virtually any recipe. It’s very popular with tomato based recipes, and can be used both fresh and dried.
Remember that fresh basil is more potent, and it’s best added towards the end of the cooking process. Dried basil is more convenient to have in your store cupboard. If you like to keep a bunch of herbs and spices to hand such as oregano, the dried basil variety will be a great alternative until you can get some more oregano.