You are welcome to that answer as far as it goes, but do bear in mind that your metabolism is a complex, complex system, and that the reply that I gave was merely a simplification of one aspect.
Actually, metabolism of your lipids, whether dietary or mobilised, involves a great deal of converting of fatty acids to and from acetate. Any fatty acid that your enzymes can handle can end up as acetate, and by far the most of the fatty acid that you build up again from acetate for storage and the like, ends up as the same saturated fatty acids, largely stearate.
In other words, if you do not eat large quantities of fats or fatty acids, your bodily fat fairly soon converges on a standard constitution.
Now, if you stop eating fat, making up for it with carbohydrates, or worse, amino acids, then the end product before final oxidation also is acetate (not counting various waste products, in particular those from the metabolism of amino acids). When that acetate winds up in either your blood or in adipose cells, it largely is metabolised into fat, and in particular into a constitution of fat typical of your body.
That is why energy-rich foods are largely interchangeable in terms of the kind of fat they produce.
The body however does not necessarily process all types of foods equally efficiently or healthily, especially if there is a sudden demand on the body to adjust its metabolism to a new, unbalanced diet. That is why the Atkins diet at first seems very effective; your body simply is not coping very well with all that perfectly good, but expensive and poorly balanced meat and similar foods. Once it does adjust, the rate of weight loss often decreases, and of course the rate of production of unhealthy metabolites increases. For such reasons, the Atkins diet tends to win a lot of converts in the first week or two, but very few that stay the course. It makes them feel lousy, it costs a lot of money, and it is diminishingly effective.
Sorry to sound so tiresomely virtuous about it, but a healthily balanced diet in appropriate quantities without snacks or excuses, together with healthy exercise, not only is the only healthy way to adjust your weight and keep it adjusted, but in the longer run it is the easiest. What is more, if you wind it up properly so that at the end of your diet you are easing into a healthily balanced, comfortable eating pattern, it is very easy to continue with that style of living without either backsliding or discomfort.
Enjoy!