Mushrooms are the fruit of a fungus and there are hundreds of varieties some edible, some poisonous. The most common mushroom found in grocery stores in the U.S. is the white button mushroom. The portobello mushroom has gained in popularity over the last several years as well as it's younger sibling, the crimini.
You can find some of the less common varieties like lobster mushrooms, matsutake (shown) and morels at your local farmer's market.