What are the differences between the philosophy of science and the philosophy of history?

Philosophy of science is more theoretical in nature, while the philosophy of history deals with events and how they happen. I will draw upon two examples that illustrate their differences:

Philosophy of science:

David Hume's Problem of Induction is an epistemological argument that states that inductive logic that can never be fully supported. That is to say that there is a risk involved when using inductive logic. Inductive logic is used daily by us, however. An example of this would be the sun has risen every day before now, so it will rise tomorrow. While this seems obviously true, it's not. Just because it happened before does not guarantee that it will happen tomorrow. This type of logic is what science is based on: what happens in a controlled experiment should happen in other experiments with the same control. That being said, while inductive logic shouldn't work all the time, it seems to with science. So, this is more theoretical.

Philosophy of History:

G. W. F. Hegel approached history in a dialectical format. A dialectic represents history as follows: A + ~A (B) = C. In other Words, Thesis (Event A) + Antithesis (Event B) = Synthesis (Event C). An example of the utilization of this dialectical method can be noted in the philosophy of Karl Marx. He insisted that there would be a rebellion of the proletariat (Thesis) against the bourgeoisie (Antithesis) to lead to a classless society (Synthesis).

Hopefully this was clear enough for you.