Without context these are fairly general terms, however
A planter can be considered one who owns a plantation which farms (usually) a specific crop on large acreage.
A farmer is a general term used for one who plants a variety of crops on land he owns or rents. This can be a small acreage to very large.
There is no hierarchy between these two terms. Although some people may consider the planter a land owner and the farmer a sharecropper working land owned by the planter.
You really have to be more specific in the context of how these are being used to get a specific answer.
hoped i answered your question :)
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