Farmers are included in OCC2010 code 0205, “Farmers, Ranchers, and Other Agricultural Managers.” Supervisors of farming workers are included in OCC2010 code 6005, “First-Line Supervisors of Farming, Fishing, and Forestry Workers.” Based on these code labels, I cannot say with certainty what the difference would be between “other agricultural managers” and “first-line supervisors of farming workers.” I would assume that farmers are not included in code 6005, since they are clearly included in code 0205. However, if you wish to determine this with a higher degree of certainty, the Census Bureau does provide documentation on occupational classification that you may find useful.
The exact set of occupation titles included in each OCC2010 code depends on the year the data are from. OCC2010 harmonizes OCC codes from 1950-2022 into the Census Bureau’s 2010 occupational classification scheme. For the year(s) of data you are interested in, I would start by tabulating OCC for each value of OCC2010 you will possibly be using (in this case, it sounds like just OCC2010 code 6005). Then, refer to the index of occupations and industries from the corresponding year of data to view the list of occupation titles included in that OCC code. You will be able to determine whether farmers are ever coded as an occupation that is harmonized into OCC2010 code 6005. You may also find the O*Net summary of this occupation code useful.
Occupation codes are industry dependent; two individuals may hold the same occupational title but work in different industries, and therefore be categorized as having different occupations in OCC. You can read more about these classification rules in the indices of occupations and industries.