"Peasant" is a very general term that have very little social meaning. Peasants were people who grew food (including raising animals) and they could include anything from a slave to rich free farmer who could himself own slaves and servants -and anything in between, depending on time period and location.

In popular culture Medieval "peasant" is associated with "serf", but that's completely wrong association.

Medieval European societies were very hierarchical, starting with very strong hierarchy in the family. "Equality" basically did not exist at all anywhere, it could only exist between people of the same social status, that is you could find it in institutions like guilds (and then only to a degree) and not places and communities.