The Definitions of Fat Components
Fats are assembled from glycerol and fatty acids.
Glycerol:

Fatty acid: a long-chain organic acid found in fats:

A monoglyceride: a glycerol molecule with one fatty acid attached. This is done by joining an OH of glycerol to the OH of the fatty acid. Rearranging the chemical bonds creates the monoglyceride, and releases a molecule of water, H2O.

A diglyceride: a glycerol molecule with two fatty acids attached:

A triglyceride: a glycerol molecule with three fatty acids attached:

This form, triglyceride, is the form in which fat is stored. Animals, including humans, usually store fat in fat cells, which is OK. Fat storage in other cells, such as the liver, is unhealthy. Fatty liver is associated with circulating triglycerides in the bloodstream; this is one of the things that is checked in blood tests.
Plants also store fats, usually, and almost exclusively, in seeds. But animals typically store saturated fats, while plants store unsaturated fats, usually of the ω-6 variety. The difference between saturated and unsaturated fats determines whether the fat is a solid or a liquid (oil) at room temperature.
Lecithin, a phospholipid. Also known as phosphatidylcholine:

Phospholipids are the form of fats that are used by cells. The phosphate and choline groups, shown here to the left of the glycerol portion, are charged. This makes this end of the molecule soluble in water. The other side of the molecule, made up of the carbon-hydrogen "tails" of the fatty acids, is not soluble in water. This "hybrid" nature -- part soluble, part insoluble -- is what makes it possible for phospholipids to form cellular membranes. It is also what makes lecithin a good emsulifying agent for production of mayonnaise, hollandaise, and bearnaise sauces.