What's the difference between determinism and fatalism?

Your understanding is actually pretty accurate.  Here is a bit of historical context to flesh it out. Both fatalism and determinism are opposed to the concept of free will, the idea that we have control, but diverge completely in terms of why.  Fatalism is based on the notion that the world is controlled by the gods, and we cannot go against their wishes, no matter how hard we try.  Expressions of fatalism include Njall's Saga, much of Greek mythology, and other stories in which the protagonist hears of some prophesy they don't like, strives heroically against it, but ends up inadvertently bringing the prophesy about through their actions. Determinism, on the other hand, became popular with the development of formal logic and again with physics.  People saw that the natural world seemed to operate according to fixed laws, noted that people were part of the natural world, and therefore proposed that people--including the inner workings of our minds, desires, "choices", and so on--also operated according to fixed laws.  Nowadays, the definition of determinism seems to have shifted somewhat to include randomness and probability, since making a decision based on a mix of randomness and physical law still does not seem like a "free choice". Fatalism doesn't make much sense without an author, but determinism can have an author or not.  The early determinists saw God as the Supreme Being that set up the grand machine that we are a part of and created the laws of nature.  However, one could also believe in a theory of the universe in which no creator is involved.  Also, in fatalism, people make choices, its just that those choices are overpowered by the wishes of more powerful entities.  For determinism, "choice" is at best a shorthand description for the result of a really complex process that is ultimately based on physical law (e.g. neurons firing), and at worst a meaningless concept.