If the hydrocarbon chain has no double bonds, then the fatty acid is saturated, as in saturated fat. If it contains at least one double bond, it is unsaturated. If it has only one double bond, it is monounsaturated, and if it has more than one, it is polyunsaturated.
Fatty acids are usually found in the body bonded to glycerol, which can bind up to three fatty acids. If all three positions are filled, then it forms a triglyceride. Glycerol with two fatty acids is a diglyceride and with one is a monoglyceride.