Pork Shoulders & Pork Butts
Here's the thing: pork butt and pork shoulder are both from the shoulder. They are, technically, different cuts, with the butt (a.k.a. Boston shoulder, and many other names with Boston in them) coming from a thicker section of the shoulder with intense marbling that makes it a darling for pulled pork and other barbecue styles and the shoulder (a.k.a. pork blade shoulder or picnic shoulder) usually being the triangular piece that would be attached to the butt. So many styles and regional variations exist in butchery, however, that it's difficult for the average consumer to know exactly where the cut is from. Luckily, both need long, slow cooking and are great barbecued, braised, or used as stew meat, so you can use them interchangeably.
Fat back, a.k.a. fatback, is, much as it sounds, the fat from the back of a pig. It is "hard fat" that can be chopped and ground (this is compared to the visceral or "soft fat" found in the abdominal cavity). As such, fat back is a key ingredient in sausages to add fat and moisture. Fat back has a rather high water content, so adding too much to burgers or meat loaves will cause noticeable shrinkage when cooked.
Pork tenderloins (a.k.a. pork tender, pork fillet) are extremely popular. They are also, along with pork loin chops, the most expensive cut of pork. They are lean, tender, and boneless. They are also easy to cook - try them grilled, roasted, or broiled - but also easy to overcook, so pay attention when they're on the fire or in the oven!
Pork tenderloins are sometimes sold with a silverskin, or silvery membrane, still attached. Remove this before cooking (or ask your butcher to remove it for you).
Leaf lard is the highest grade of lard (lard is pork fat, the term is usually used to refer to rendered pork fat suitable for cooking). It comes from the visceral, or "soft," fat from around the kidneys and loin of the pig. It lacks any real pork or meaty flavor, making it an excellent neutral-flavored cooking fat with a high smoking point. Leaf lard is particularly prized by bakers for use in producing moist, flaky pie crusts. Learn more About Leaf Lard here.