First of all, the thing to realise is that both of these theories have the same result in the end. They both mean that how our life ends up is decided by forces other than ourselves. But the difference between the two is in how the direction of our lives is decided.
In fatalism, we have one true "fate" and we will end up there no matter what. Our life may take whatever journey it want, but we cannot escape our eventual fate. What exactly decides this fate is different depending on the version of fatalism we are discussing. For example, some people might believe that we have a fate that is decided by a God, but this is just one version of fatalism. Determinism, on the other hand, means not only that we have one pre-decided fate that we will end up with, but also that every event in our life is decided by earlier events and actions. In short, fatalism is the theory that there is some destiny that we cannot avoid, although we are able to take different paths up to this destiny. Determinism, however, is the theory that the entire path of our life is decided by earlier events and actions.