Peasant isn't and never was a synonym for "poor person." It refers to a social class consisting of agricultural laborers and small farmers, the majority of whom just happened to be poor (this is true of all social classes in premodern European society - not all nobles were necessarily rich). A penniless beggar living in a town would not be considered a peasant, while a well-off farmer in an agricultural village would. Thus, historians do use the words peasant and peasantry to refer to the agricultural laborers inhabiting the countryside in pre-industrial societies.