Even within a caste system there is still some mobility within the caste. Humans, like many other animals, seem to automatically generate some kind of hierarchy whenever there are more than a couple together, even if it isn't a fixed one (there may be several together, used for different purposes or in different places; the hierarchy for breeding rights may not be the same as for giving orders when working, and both may be different from that in a social context).

I would say that a rigid caste system is one form of inequality, but not the only one. A total inequality wouldn't necessarily say that one couldn't marry below one's station, for instance, or determine the status of children by the position of their parents, it could for instance be a meritocracy where one's position was determined only by the calculated value to society of that individual, and for genetic reasons it might even be required that a person breed at least a certain distance above or below them (since no one would be exactly equal to anyone else they obviously couldn't breed with an equal). 'Doc' Smith had something like that in his posthumous Family d'Alembert series, the royalty were required to marry commoners to avoid inbreeding.