Sweet potatoes have sweet orange flesh that cooks to a moist texture (they're often mislabeled "yams," a starchier vegetable).
Round white potatoes are waxy-fleshed potatoes with more moisture and less starch than russets or golden potatoes.
New potatoes are young, very thin-skinned, waxy-fleshed potatoes that are low in starch. They can be of any variety.
Round red potatoes are like round white potatoes, with waxy flesh, and are good for boiling. They are low in starch.
Russets are high in starch and the ultimate baking potato, with a dry, fluffy texture.
Golden potatoes have yellow flesh and are all-purpose potatoes; Yukon gold is a popular variety. These are medium-starch potatoes.