Politics means the world of government in general:
The vice-president has a long career in politics.
I hate discussing politics with my family because it always turns into an argument.
Sometimes people talk about "office politics" outside the context of government -this means the connections and actions that people inside a company take in order to gain power, forming relationships and manipulating situations to their advantage.
A policy is like a rule. Countries have policies (foreign policy, immigration policy, gun control policy) but schools and companies do, too:
Our policy is that customers can return an item and get a refund within 30 days of their purchase.
My school had strict policies regarding lateness - if you were late more than five times, you got suspended.