They are about the same thing. Usually no one bothers with such nuances. Because the manufacturers of dietary supplements are not very controllable and mix the two types of fat.
Fish fat
This is the name of the traditional fish oil, which is extracted from the liver of fish. In addition to health benefits omega-3 unsaturated fatty acids such fat also contains many fat-soluble vitamins. For the sake of these vitamins, children used to be fed a spoonful of smelly fish oil.
Now there is also such a fashion that if, in addition to omega-3 fatty acids, you would also like to receive vitamins A or D, then eat fish oil, which is obtained from fish liver.
But it's not good enough to swallow excess chemicals. The fact is that the liver of fish accumulates all sorts of pesticides and other toxins from the water.
Fish oil
This is a more technological fat, which is obtained from a whole fish carcass. And in different industrial ways. It is unlikely that someone will specifically take out the fish liver from there.
For this purpose, they process any small fish that no one will specially gut for you. By various chemical and physical methods, fat is released from there, in which there will also be some amount of chemicals, but less than in the fat obtained by sight from the liver.
This fat is safer. It is simply called fish oil. Not fishy, but fishy. And the one that was from the liver is called "fat from the liver". Play on words. You can get confused.
The doctors decided that by using any dietary supplement with fish oil, you can run into toxins. But in the recommended daily amounts of fish oil, these chemicals will be so small that you can not worry. So no one really bothers.