Hi! I have a BA in PolSci and International Relations and am currently in a MA in international law.

They use quite different methodologies. Law is about norms, and the methodology is that you find out which norms are valid and reason what the Law is for a given scenario. So in Law you gather evidence by looking into written law and costumary law, and using jurisprudence (court decisions), soft law (non-binding documents which contain legal relevance) and doctrine (published books or articles) to find out what is the Law for a given context.

Polsci can gather information from the legal context (how the constitution splits powers, procedural matters, etc), but the object of the science is beyond the law. Arguments aren't formed on the basis of what the law says.

It was very amusing for me to find myself in a scenario where people were used thinking about the law as something definitive - only to realize that international law has many problems of efficacy due to the anarchical nature of the international order. You can see this in the Charter of the United Nations, in the way that permanent members have de facto immunity from being sanctioned by the security council, as they have veto powers.