More simply saturated fat is solid at room temperature while unsaturated fat is liquid. While animal fats tend to be saturated and vegetable unsaturated coconut and palm seed oils are saturated vegetable oils.
What makes fats saturated or unsaturated is the number of hydrogen atoms bonded to the carbon atoms in the fatty acid chains. Years ago they discovered that if they broke the double carbon bond in fatty acids in vegetable oil and bonded the carbon atoms with hydrogen that liquid vegetable oil became solid. This is called hydrogenated oil. Most vegetables shortenings used to be partially hydrogenated vegetable oil. Since the fatty acids are not fully saturated they are called trans fat.
When I was in high school chemistry in '78 my teacher warned us about partially hydrogenated vegetable oil. At the time vegetable shortening was sold as a healthier alternative to butter or lard. My teacher warned us that hydrogenating vegetable oils made them just as bad for us as saturated animal fats. While his advice was far ahead of its time it turned out that he didn't go far enough. Now we know that trans fats are much worse for us than lard or butter.
I recently noticed that "hydrogenated vegetable oil" is listed in some products that brag to be trans fat free. Now food makers are using fully hydrogenated vegetable oil in products. Fully hydrogenated vegetable oil is not a trans fat and food producers claim that fully hydrogenated vegetable oil is not unhealthy but considering that they were wrong about partially hydrogenated vegetable oil 50 years ago I'm inclined to be skeptical about their claims for fully hydrogenated vegetable oil now. I prefer natural fats untouched by chemists.
Saturated fat is a type of lipid that is derived from most animal products. Scientifically, it carries a double bond of saturated fatty acids and lipids with carbon and is solid at room temperature. You can usually tell by the "white" part of meat, which is indeed saturated fat because it is a solid. Most people will say this fat is bad, but the body needs saturated fats, just in a proper amount. To regulate balanced hormone function, make sure 3-5% of your fat intake is saturated fats. For instance, if you needed 70g of fat a day, 21g of that would be saturated fats.
Unsaturated fats are similar, but only carry one or two bonds with carbon in an unsaturated fatty acid. This type of fat is helpful to maintaining proper insulin spikes, organ health, and prevents inflammation.This type of fat also requires less energy to burn so they're easier to burn than saturated fats. They also serve to maintain High-Density-Lipoprotein (HDL) which is a form of good cholesterol.
Trans fats are like a cross between unsaturated and saturated fats. Trans fats all start out as unsaturated fats, and with the addition of hydrogen atoms, they become saturated. These fats lower HDL and raise Low-Density-Lipoprotein (LDL) which is bad cholesterol. You can find most of these in french fries, cakes, and donuts. If you see "hydrogenated oils" as an ingredient, that symbolizes that the unsaturated fats have been bonded with another carbon atom and a hydrogen atom to increase saturation.
Healthy saturated fats:
Healthy unsaturated fats:
*White meats like Chicken or turkey
The value of each type of fat in the human diet is still widely debated. People in the Weston Price cult believe that saturated animal fats and cholesterol are almost a panacea while others point out that our bodies can make all the cholesterol and saturated fats it needs and that there is no dietary requirement of either. Most studies have leaned in the favor of reducing saturated animal fats including ones you list as healthy. High consumption of animal fats is a risk factor for dyslipidemia as well as breast, ovarian, colorectal, and prostate cancers.