Sweet potatoes are shorter and fatter than yams and are sweet and moist, while yams are starchier and drier. Sweet potatoes also have a smoother skin, where yams are kinda scaly, and have lots of beta-carotene, while yams have very little.

This is a tricky question and a first glance at the web sites may be confusing. There are actually three different sorts of vegetables that need to be distinguished.

The classic American dilemma of what is a sweet potato vs a yam and which is better comes down to this: The "Yam" best known in America is one of several varieties of sweet potato which can be distinguished by dark orange skin, orange flesh and a very sweet flavor. Ordinary sweet potatoes have a thin yellow skin and light yellow flesh, and are less sweet and closer to regular potatoes in texture. My dad always said to be careful to choose yams.

However, the world is becoming smaller every day. In Africa and the Caribbean and Asia the True Yams are grown. There are at least 200 kinds and some of them are now imported to American grocery markets. They have brown or black skin and a variety of colors of flesh including white, purple, and red. These are an unrelated vegetable but in cooking are quite similar. Perhaps confusingly, the true yams are more similar to Sweet Potatoes than they are to Yam Sweet Potatoes in that they are less sweet, more starchy.
Below the American Yam Sweet Potato is on the left, the Sweet Potato on the right. True Yams are in the second photo.