As set out in the Statute, crimes against humanity include crimes such as the extermination of civilians, enslavement, torture, rape, forced pregnancy, persecution on political, racial, national, ethnic, cultural, religious or gender grounds, and enforced disappearances - but only when they are part of a widespread or systematic attack directed against a civilian population.
The "widespread or systematic" qualification for crimes against humanity is very important, as it provides a higher threshold, requiring a particular magnitude and/or scope before a crime qualifies for the Court's jurisdiction. This differentiates random acts of violence - such as rape, murder, or even torture - that could be carried out, perhaps even by soldiers in uniform, but which may not actually qualify as crimes against humanity.
War crimes include grave breaches of the Geneva Conventions and other serious violations of the laws and customs that can be applied in international armed conflict, and in armed conflict "not of an international character", as listed in the Statute, when they are committed as part of a plan or policy or on a large scale