Spackle is made of gypsum, a natural mineral material that is combined with various mixing agents. Originally spackle was a powder that a user mixed with water. It still is available in that form, although the most common type today is premixed. Muralo developed a lightweight version in 1983 and subsequently created one that is pink when installed but turns white when it is dry and ready to be sanded and painted.
Plaster today is a combination of Portland cement and some fine aggregate, sometimes lime, sometimes very fine sand; horsehair and other fibers once were used as aggregate. It typically is sold as a powder to be mixed with water. It can be shaped and formed and dries to a very hard surface. It is closely related to stucco, a cement and lime or aggregate material frequently used on exterior walls.
Spackle is used mainly to patch nail holes and small cracks or damaged spots in drywall. It dries quickly, does not shrink when dry, can be "feathered" to conform to undamaged wall surfaces and sands easily. It is primarily used indoors, but Muralo and others have developed versions for use on exterior walls. Spackle can be used to repair small blemishes in plaster walls and also on wood surfaces but is primarily used with drywall, which also is made with gypsum.
Plaster is used to repair large breaks or damaged spots in plaster walls, which typically are installed over wood or metal lath. It should not be used to repair drywall or fill holes in wood surfaces. Plaster patching requires more preparation; old or damaged material must be stripped down to the lath base, then plaster is spread over the damaged area with a trowel.
Drywall compound or mud is similar in material and texture to both spackle and plaster, but usually is used only to cover seams and nail holes in drywall. It does not bond permanently to plaster and should not be used to patch large areas in plaster walls. It can be used to fill nail holes in unpainted drywall, but spackle is better for repairing damage in existing walls.