The term peasant referred not only to the amount of wealth a person had but also their rights and job. Peasants often didn't own the land they worked, instead renting it from nobles. Sometimes peasants were thought of as only a little better off than slaves, which is quite different from poor people in many parts of the world today who, even though they're not wealthy, still have many rights. Another defining characteristic of peasantry is a lack of social mobility, especially in places like medieval Europe. I'm not sure how peasants in other areas of the world were treated, but in medieval Europe they were forbidden from adopting a status other than that of a peasant. Also, peasants are always farmers so it wouldn't make sense for a factory worker or retail store employee to be labelled as a peasant.