Yes, my outline was very general - in reality, it will not always be "black and white". For instance, peasants are not necessarily all "slaves" or "servants". Many peasants, as Panjandrum mentions, are able to gain wealth. A prime example of this would be the Kulaks of Russia, who were perceived as being capitalists, due to their attained wealth. These men were considered "peasants" in the sense that they did not really have a social status, although they could also be described as farmers, due to their occupation and independence.Andreyevich has given a very useful generalisation.
There are variations in usage of both peasant and farmer that make the difference difficult to define without context. The OED extracts below illustrate this.
A person who lives in the country and works on the land, esp. as a smallholder or a labourer;
In specific contexts the term may be variously defined. Although modern sociologists agree that a peasant works the land, the more wealthy peasants may also be landowners, rentiers, hirers of labour, etc., and in these capacities share interests with completely different social groups.
One who cultivates a farm, whether as tenant or owner; one who ‘farms’ land, or makes agriculture his occupation.
That might be why farmers are considered to have more status, I suppose. Doesn't have that a negative ring, though less than "boor"?"(…) the distinction was that a peasant (synonym serf) is landless, and is employed by the landowner, with few if any rights. See #3. Russian peasants became collective farmers at the Revolution, though whether their material status changed I don't know. A farmer is independent, self-employed, whether he owns the land or rents it.
There are still landowners in France who seem not to have realised this. The local marquis was brought up in court a few years ago for trying to insist that his tenant farmers buy their feed and fertiliser through him, not on the open market. He lost the case.
In a roundabout sort of way.I read that boor comes from the Dutch for farmer 'boer'. .
Persons fitting that description in Latin America still are referred to as "peasants," although that usage might be declining in politically correct usage.I have been trying to find out the etymology, but I seem to run into trouble because the 'farmer' concept does not seem to be universal (not everyone combines tilling the land with animal husbandry). The other aspect is that some words like 'peasant' have a pejorative ring. I suppose it is not always the case with "peasant", or is it?