Some Pepos are eaten in the immature stage as thin-skinned summer squash. Most traditional Jack-o-lantern carving and baking pumpkins are of the Pepo species. Acorn squash and spaghetti squash are also part of this family. They have distinctive hard woody stems that have furrows in them. The pumpkins in this family are a deep or bright orange.
Maximas can get huge, and keep fairly well in storage. You can usually tell them from a Pepo or Moshata in that they have a spongy cork-like stem. Most winter squash are also part of this family. Varieties include Pink Banana, Buttercup, Hubbard and Turban.
Moshatas are excellent keepers. Their flesh is usually orange in color, sweet and refined. They store extremely well and are well suited for a multitude of recipes. Their stems are smooth and have deep ridges. Examples are the Cushaw Green and Gold and Butternut. Their color is usually tan or cream and they are elongated in shape.
Mixtas typically have pale yellow or cream-colored flesh. They are usually not quite as sweet or refined as a Moshata or Maxima. They are often stuffed or baked with brown sugar or maple syrup to complement their flavor. The above descriptions are general and I have found there can be many exceptions. Mixta are also known as argyrosperma.