No, this isn't going to be as gross as it sounds. LOL
I will show some contrasts between essential oils and fatty oils from plants. This is all still coming from "The Chemistry of Essential Oils" by Dr. David Stewart.
Essential oils can be found anywhere in a plant, i.e. the stems, leaves, roots, seeds, etc. Fatty oils, which are also called vegetable oils, cooking oils, massage oils, and fatty "acids", are only found in the seeds of plants. For example, lauric acid, a fatty oil, is found in the seeds of the bay laurel tree, while laurus nobilis, an essential oil, comes from its leaves.
The molecules of fatty oils look like chains connected by carbon atoms at each link. The long chain structure is what makes these oils feel greasy. Essential oil molecules are usually more like hexagons and octagons. Their more rounded structure keeps them from slipping around on your fingers.
Fatty oils are not used by an adult plant as essential oils are. They are expressly for the next generation. They are used for germination and sprouting, and feeding the young plant until water and sunlight are available. Their larger molecules prevent them from circulating through plants and human bodies, and from passing through cell walls as essential oils are able to do. They are greasier than essential oils, and they can turn rancid. They are not antibacterial, antiviral, anti fungal, anti parasitic, or antiseptic as essential oils are.
There are two exceptions to this (that I personally am aware of), which are coconut and olive oils. These two fatty oils also have some essential molecules and are therefore slightly therapeutic while also being nourishing to the skin.
There are two main categories of fatty oils: saturated and unsaturated. Saturated means the molecules hold all the hydrogen atoms possible for each. There are only single bonds between each carbon atom when this is the case. There can be multiple bonds between carbon atoms and other types of atoms, just not between two carbon atoms. Unsaturated means there are one or more double bonds between some carbon atoms.
There are pictures of the molecules which maybe I will draw and scan in so you can see that even when a molecule has the same molecular weight as another molecule, it is the actual shape of the molecule that determines its distinct characteristics.
It is interesting to note that just as essential oils perform the same tasks in human bodies as they do in plants, so do fatty oils. Fatty oils are used for food for the seeds of plants, just as they are commonly used in our food.
Fatty oils are beneficial outside of the body as well. Because they do not penetrate the skin they are able to form a protective barrier against the elements. This is one reason why they are softening to the skin and used as moisturizers. Tamanu is a fatty oil which has been used for centuries as a natural sunscreen and moisturizer combined.
In application, if fatty oils are being used, they should always be applied after essential oils are applied. The molecules of essential oils adhere to the molecules of fatty oils, so by applying the fatty oils afterwards, you are giving the essential oils a chance to get into the body faster and sealing them off from evaporation. This principle can also be used to prevent injury. Some essential oils can get very warm on the skin as they pass through the cells at lightning speed. The smaller molecules of the essential oils group up on the large molecules of fatty oils, which causes their trip through the skin to slow down a little. I always have a vegetable oil on hand when using "hot" essential oils on children, and on more sensitive areas of the skin so that I can apply it if necessary to "cool" the site down. WATER SHOULD NEVER BE USED IN THIS TYPE OF SITUATION. It will drive the hot oil into the skin faster and create more pain.