The difference between egalitarianism and hereditary monarchy lies in the fact that It creates conditions for people to be equal, despite familial ties.
Egalitarianism refers to the idea that all classes function as an equal society whereas a hereditary monarchy consists on the succession of rulers based on bloodline instead of providing everyone an equal chance.
Egalitarianism is a school of thought that prioritizes equality for all people. Egalitarian doctrines maintain that all humans either should "get the same, or be treated the same" in some respect, including social status.