A heel is the bottom, back part of a shoe or boot that provides elevation. The styling and construction of a heel may vary (i.e., stacked, stilletto, spiked, sculptured, kitten).
About Pumps:
Pumps are heeled shoes that are typically tapered to a point or a narrow square toe. The upper of a Pump covers the heel and sides of the foot, leaving the top of the foot exposed, which allows the wearer to slip on the shoe.