At this point in time it's the common-uncommon knowlege that the things called yams in the US are actually orange sweet potatoes. There's already a ton of history but long story short is orange sweet potatoes were grown in the 1930 and were called yams beacuse they looked like African yams. But it's just not the Americans that messed up. Australia, New Zeland and Malaysia, Singapore and Portuguese speaking countries also calls things not yams as yams. But the question remains what's the difference between a sweet potato and a real yam?
Potatoes are all of the Solanum tuberosum species. Sweet Potatoes are of the Ipomoea batatas species (at least the edible ones are).
So Sweet Potatoes and Potatoes are both memebers of the Solanales Order but have different Family, Genus and Species.
Yams are of a bunchload of different species but they all are of the Dioscorea Genus. If you were being very generous (or maybe drunk) you could be lead to believe something like the Yellow Yam or West African Yam is a (sweet) potato that went awry. With it's larger size, slightly hairy exterior and dryer interior it's not THAT far off the mark from a sweet potato. However cutting into a Mountain Yam aka Chinese/Korean/Japanese Yam aka Nagaimo ("Long Potato") aka Yamaimo ("Mountain Potato") will quickly greet you with a snot like consitency and make you realize indeed, this is not a potato or sweet potato, if the funny oversized parnip like appearence wasn't enough of a clue.