These are immature potatoes that get thinned out early in the season order to make room for the rest of the potatoes to mature. New potatoes aren't a variety by themselves, but are simply the baby version of any potato a farmer grows. In fact, those being sold as "baby" potatoes are the same as new potatoes, or slightly more mature.
New potatoes are round or oblong in shape and can range from the size of a walnut to the size of a ping-pong ball. Since new potatoes harvested so early, their skin is very thin and tender, often feathering or peeling off in places. New potatoes don't need to be peeled before cooking and are great roasted or boiled. They have a delicate, slightly sweet flavor and a creamy texture.
Also, since their skin is so thin and new potatoes haven't been hardened, they are more perishable than regular potatoes. They can be stored in a paper bag in a cool place like mature potatoes, but should be eaten within a few days of purchase.
Fingerlings are their own variety of potato, though they often get confused with new potatoes because they're also quite small. Fingerlings are fully mature and get harvested after the green upper portion of the plant has died back.
They are elongated potatoes generally the size of a finger (truly!) with knobby bits down its length. Also like new potatoes, the skin is very delicate and doesn't need to be peeled before cooking. The flavor is closer to the regular, mature potatoes we're used to and they have a firm texture that holds up well to cooking. Try them roasted whole or boiled.
For us, the biggest draw to both new and fingerling potatoes is their unique shape. We like to use them in recipes that show case their tiny stature, like potato salad or a simple roasted side dish.
Do you love these little tubers, too?
Related: Sixteen Kinds of Potatoes