Law is defined differently by different schools of thoughts. Some attribute more importance to one element of law than the other elements. For example positivists define law as a command of state that is backed by the state's enforcement power. They are in the opinion that without the power of enforcement, no system of rules can be regarded as a system of law.
Although different definitions law exist, it in general terms, can be described as the body of rules, whether proceeding from formal enactment or from custom, which a particular state or community recognizes as binding on its members or subjects.
Internatioanal law is defined as a set of rules and principles created between states ans instutional subjects of internatioanal law such as the UN, either for their own purposes or as a means of facilitating the functions of organisations of which they are memberes.
There are clear differences between international and national law. National law has a supreme authority, and based on principles of command, obedience and enforcement. There are law making, law determining and law enforcement agencies. However, International law lacks a supreme authority. States are legally equals. It is based on consent and reciprocity. There is not any enforcement institution. .
The nature of international law.
The creation of public international law relies on negotiation and ratification of formal treaties and conventions, and on the formation of custom. Customary international law arises through the "general practice" of states" legally relevant actions resulting in stable expectations, and ultimately in rules widely believed by states to be legal requirements. This is to be contrasted with international law arising from treaties or other formal legal arrangements, which are negotiated by states, and must be signed and ratified in order to be considered legally binding upon a state. States cannot fail to participate in the formation of customary international law concerning their behavior, as it is a product of long term, legally relevant interactions.