There's an easy way to tell the difference between sweet potatoes and yams: If you picked up the tuber from a typical American grocery store, it's probably a sweet potato. Almost all of the foods most of us think of as yams are really sweet potatoes. The root vegetable typically has brown or reddish skin with a starchy inside that's orange (though it can also be white or purple).
Yams are a different beast altogether. They are more closely related to lilies and grasses and mostly grow in tropical environments. The skin is more rough and bark-like than what you'd see on a sweet potato, and the inside is usually white or yellowish—not orange.
If you want to know more, check out this great article from Mental Floss on both sweet potatoes and yams!