The international definition of the crime of genocide is supplied by the 1948 Convention on the Prevention and Punishment of the Crime of
Genocide. It proscribes a collection of acts
...with intent to destroy, in whole or in part, a national, ethnical, racial or religious group...
The "in whole or in part" clause gives some breadth to what can be considered genocide, legally.
Since your question is about the political use of the term, the legal definition rapidly becomes meaningless since political speech has never been truly bound by legal definitions of any kind and instead obeys the rules of rhetoric. Genocide, therefore, gets tossed about roughly as loosely as 'terrorist,' insofar as it is important to note the distinction between someone's rhetorical bloviation and an actual legal claim when understanding how each term is being used. (See This question for more examples of this.)
"Crime against humanity" doesn't have a clear pedigree in the same way, but is inclusive of genocide, terrorism, piracy, human trafficking, and other large-scale insults to the dignity of the common human condition. It's lack of specific codification makes it ripe for rhetorical convenience.
The definition of fundamental human rights co-evolved alongside these terms, and isn't directly informative to them per se, but would definitely be relied upon by any prosecutor trying to make such a case in court, particularly Article 3:
Everyone has the right to life, liberty and security of person.
and when necessary, Article 4:
No one shall be held in slavery or servitude; slavery and the slave trade shall be prohibited in all their forms.