Fatalism is the doctrine that events are predetermined by forces that human beings cannot control and that every event must take place. The idea of free will would be an illusion as we have no choice in our actions and that there is no alternativeness in our futures if our futures have already been inexorably fixed. A fatalist therefore believes we are unable to change the future or past as it's already been set out for us.
Determinism on the other hand, argues that events occur due to cause and effect. It disputes the claim that the future as we know it is fixed but it can be changed as a consequence of a set of causally related events.
With both fatalism and determinism, there are certain extremes. There are soft and hard fatalism as well as soft and hard determinism. Soft fatalism is the belief that not all things are fixed and hard fatalism is where everything is fixed.
Soft determinism is where some events are consequence of cause and effect but not all where hard determinism is the belief that all events are determined by cause and effect.
When one is a fatalist, one can still argue as a determinist as it is predetermined that one cause would in turn produce a consequential effect. The effect would be predetermined according to the cause. Thus, it can be said that even a fatalist could be a determinist. Yet this would have to mean that only one certain effect could occur as a consequence of a cause or action as it has be predetermined. For example, I hit my cat and it bites me. It is easy to conclude that perhaps I was predetermined to hit my cat and the predetermined effect of hitting my cat would be...