Its a common belief that fat is fat, whether we eat it or whether its stored in our bodies. Of course this is naive, our bodies are far more complex than skin balloons packed with nutrients. There are two kinds of fat tissue in our body;
The "fuel silos" are called White Adipose Tissue (WAT) made of simple cells; their membrane has a few receptors on it that trigger the cell to store or release energy, the nucleus is small and pressed against the cell membrane, and inside one big lipid droplet that shrinks or swells as needed. When dieting your pancreas releases Glucagon to trigger your fat to release their reserves. When your body releases insulin (which it does after almost every meal to some degree) your WAT cells swell back up. This is why its so hard to keep weight off.
Then there's the factory fat cells, Brown Adipose Tissue (BAT) which are much more complex; they contain many smaller lipid droplets and the enzimes needed to burn the energy right in them. They're especially important in infants because they're too small to shiver to get warm, so their "brown fat" burns their fat immediately to keep their body temperature regulated. Adults maintain a good amount of it in our upper back and neck, though strangely lean adults have more BAT than obese adults.
When our bodies become hypothermic, say by taking an ice water bath, BAT thermogenesis is activated depleting those cells of stored energy to produce body heat. Shivering also releases more energy to raise heat. While the sound of a ice water bath may sound horrifying, its actually not that bad after you've been running, decrease water temp slowly, and can even be meditative.
The goal is to destroy WAT (White Adipose Tissue) - not just slowly deplete it but leave the cells in a state ready to swell back up every time you eat, but actually reducing the number of white fat cells in your body for permanent weight loss.