Quick. Farmer is the man who owns the farm, and works on it. (they dont necessarily have to own it, but these days thats how it usually is) Peasant is more like a low class individual who the farmer puts to work.. we dont usually use the word peasant anymore.

'peasant' implies low social class, poor, ignorant. Calling someone a peasant to their face is most likely an insult. (although it may be true). I think the word peasant also implies that the speaker is a higher social class than the peasant. Most americans think of peasants during the Medieval times or in history rather than in the present world. 'Farmer' is a much more neutral acceptable term.

Do you mean during medieval times? If so look at: 'The average peasant in the feudal structure could be grouped into two main professions: farmer or craftsmen. The farmers worked the fields daily, planting etc' library.thinkquest.org/10949/fief/hipeasant.html

Farmer is profession. For me the word: peasant is more like mental state being. For me it means ignorance, stupidity, mental poverty, simple-mindedness, naivity, following backwards social customs slavishly, the lack of independent thinking. Person could be really wealthy but still have "the mind of peasant". Pleb in UK slang (coming from Latin world for common people "plebeii") means the same aka stupid person... person of inferior intelligence.