How do slavery, caste, estate, and class systems of social stratification differ?

The difference between these forms of stratification has to do with the degree of mobility people within these categories experience. There is also the matter of how one moves within these categories. In other words, what is the mechanism by which a person (or family) moves from one category to another?
In a caste-based system, there is virtually no mobility. Whatever caste a person is born into is the caste that they will remain in through life. In a caste-based system, heredity is what determines what category you belong to. Whatever caste your parents belong to is the caste into which you will be born.
In an estate-based system, mobility is likewise virtually nonexistent. Whatever estate you belong to at birth is likely the one you will remain in throughout life. There is a strong hereditary aspect to estate-based systems as well. However, within an estate-based system there are certain social institutions (such as the monarchy or the church) that may be able to grant you standing in a higher estate. For example, a peasant could be appointed into the knighthood, thus increasing the standing of himself and his progeny.
Traditionally, class-based systems of stratification would offer the highest degree of mobility. In class-based systems, a person's standing does not depend so heavily on heredity. It is mostly tied to how one participates in capitalism (as a laborer, as a merchant, as a capitalist, and so on). Within class-based systems, a person who changes their relationship to capitalism may experience social mobility and a change of class standing.
In a system based on the institution of slavery, there may be some limited mobility or there may not be. It depends on the particular form of slavery and on the enslaved person's unique circumstances. An enslaved person may run away, buy their manumission, or be manumitted by some other means. However, slavery as a system of stratification is typically based on strict constructs of race, nationality, or cultural/ethnic identity. Since slavery coexists alongside colonialism, empire, and other systems of social exploitation, social mobility for an enslaved person is typically extremely restricted, if there are opportunities for it at all.