I'm not sure if you are looking for an alternative general term that can describe the entirety of the common people of pre-industrial Europe, or if there are other ways which historians can use to identify individual people. If the latter, then yes, it is possible to be much more precise about the social position an individual person held within peasant society. The term peasant or commoner is not necessarily a pejorative term, simply referring to people who are neither noble nor members of the clergy. In France, they composed the menu peuple or the Third Estate, the First and Second referring to the clergy and the nobility respectively. These are however very expansive "ideal" categories that don't quite capture the diversity within each. The overwhelming majority (upwards of 90%) of people in pre-industrial Europe were peasants. Among the peasants, therefore, there were a multitude of different social distinctions and hierarchies that better specify their identity.

In sixteenth and seventeenth-century France, the experience of common people would have differed greatly depending on whether they lived in either a village or in the countryside. Most peasants were agricultural workers who lived in the countryside. Small-time peasants, or manouvriers, worked relatively small plots of land and may have even had to work other peoples' lands in order to produce enough food to survive or pick up other kinds of work on the side. The larger farmers for whom they worked were often themselves simply more prosperous commoners, called (misleadingly) the laboreurs or, in England, the gentry class. Some of these latter ones may have been even more wealthy than the lesser members of the nobility.

In the towns, artisans would have identified themselves based on their membership in the corporate bodies that represented their profession and their rank within it (i.e. journeyman, master). Different artisans would have been valued more highly depending on what they produced, their wealth, and their centrality to the community. A significant number of the population of commoners also worked as servants. The bourgeois citizens of towns could be enormously wealthy as a result of their trade or involvement in other entrepreneurial activities but still would be grouped with the other commoners within the Third Estate--although it becomes possible over time for members of this group to purchase a noble title through venal office-holding. The same goes for most members of what we would call the "professional," university-educated classes--physicians and lawyers--who also usually did not come from noble birth.

In any case, while technically all of these people fit the category of a "commoner," not all of them were land-bound agricultural workers and even in this case it matters where they fit into the hierarchy of landownership. This will vary enormously based on region and time period--I'm just giving examples from the one I know best. Unless referring to the "peasantry" as a collective whole, it is probably best to be as precise as possible when speaking of individual persons and use the terms in which they would have understood themselves.