A fat is a lipid with three fatty chains linked by an ester linkage to glycerol.

A fatty acid consists of a hydrocarbon chain (carbons bound to hydrogen), with even numbers of carbons from 4 to 28, and a carboxyl group at one end. A triglyceride consists of three fatty acids with their carboxyl end bound to glycerol via an ester bond.

The heads of phospholipids contain a glycerol group and a phosphate group. Both of these groups contain atoms other than hydrogen and carbon, so they are not hydrocarbons. Since phosphate is negatively charged, and glycerol contains oxygens, this part of the molecule is water soluble. In other words, it is hydrophilic, lipophobic, and polar. 

Phospholipids are arranged in bilayers with the hydrophilic heads of pointing out towards the aqueous solutions inside and outside the cell. The hydrophobic tails point towards each other and are in the interior of the membrane. This unique structure allows cells to be water soluble, yet have a protective membrane that is selectively permeable to small, uncharged, hydrophobic molecules such as gasses and steriod hormones. Micelles are spheres of fatty acids in solution, where their heads are on the surface of the sphere, and their tails aggregate in the center of the sphere, avoiding the aqueous environment. Micelles are usually formed by lipids with single fatty acid tails, not two, as is seen in phospholipids. 

A phospholipid has two fatty acid tails, which consist of hydrocarbons with even numbers of carbons ranging from 4 to 28, and a phosphate group attached to a glycerol head, which is hydrophilic. Monoglycerides contain only one fatty acid chain bound to a glycerol head, and triglycerides contain three fatty acid chains. 

A fat (triglyceride/triacylglycerol) consists of three fatty acids linked to glycerol. A phospholipid consists of two fatty acids and a phosphate group linked to glycerol. Thus removing a fatty acid from a triglyceride and replacing it with a phosphate group will yield a phospholipid. Diglycerides contain similar structures to triglycerides, but only have two fatty acid chains bound to the glycerol head. Steroids are lipids, but do not contain fatty acids. Rather they contain four hydrocarbon rings, and they are all derived from cholesterol. The saturation of a fatty acid refers to the presence of hydrogens anywhere they can potentially be present. A saturated fatty acid is said to be saturated with hydrogens.

The tails of phospholipids consist of hydrocarbons only. Thus they are nonpolar, hydrophobic, lipophilic and fat-soluble.  

The tails of phospholipids are hydrocarbons and are thus hydrophobic so they point towards the interior of the membrane to avoid contact with the aqueous solutions of the cytoplasm and the extracellular fluid.  

Cholesterol is class of lipids known as steroids. All steroids have four fused carbon rings in their structures. Fats, fatty acids and phospholipid do not contain any ring structures. Fatty acids are components of both fats and phospholipids and are long chains of hydrocarbons. Phospholipids contain two fatty acids attached to a polar head and a phosphate group.

The heads of phospholipids are hydrophilic and so they will face the exterior of the cell membrane in order to interact with the aqueous environments of the extracellular fluid and the cytosol. The hydrophobic tails will face the interior of the membrane to avoid water contact.