What are the different kinds of fats?

All foods containing fat - even pure oils - contain a mixture of three kinds of fat:

saturated
polyunsaturated, and
monounsaturated.

Foods are often identified by their predominant fat; for example, olive oil as “monounsaturated” butter as “saturated” – but all real foods contain mixtures of the three.

All three types of fats are necessary and important to human health and should be incorporated into the diet in a balanced proportion. The question is, what ''is'' balanced.

Saturated fat, particularly in the absence of high carbohydrate intake, is not dangerous to human health — on the contrary, when balanced with mono and poly-unsaturated fats in a controlled carbohydrate dietary environment, saturated fat may actually have real and measurable benefits in a number of different arenas. Saturated fat is quickly oxidized to energy, once you are keto adapted. So you can enjoy plenty of butter and animal fat guilt free. Interestingly, coconut oil is something very different: it consists of Medium Chain Triglycerids (MCT) which cannot be stored by the body, it has to immediately oxidize it. That means when you eat coconut oil, your body will immediately produce ketones, even when you are not keto-adapted. Nevertheless this does not mean you are getting all the metabolic advantages that you would get when keto-adapted state.
In addition, the benefits of monounsaturated fats (like olive oil) are well known and well documented.
Fats high in polyunsaturated fats, like vegetable oils, usually contain a lot of omega-6, and very little omega-3. The ideal ratio between omega-6 to omega-3 is 2:1 to 1:1, and in general this ratio is often 20:1 or even worse. It is therefore important to avoid oils high in omega-6, like corn or soy. Vegetable oils that are rich in omega-3 contains it in the form of ALA which the body has to convert to DHA and EPA to be of any use. The conversion is highly inefficient, so in practice ALA omega-3 rich vegetable oils like flaxseed oil or canola are no good choice either. The best way to get omega-3 is through fatty fish like salmon, or with a DHA + EPA supplement.

As a general rule of thumb, avoid fats high in omega-6, and run like hell from highly processed fat(anything that says "hardened", or contains trans-fats) like margarine. Eat foods naturally high in fat like meat, fish, and nuts; use plenty of olive oil, butter. In fact 50% butter with 50% olive oil approximates quite closely the composition of body fat - meaning that this is the type of fat that the body can make best use off.