Γεωργός is a bit more "narrow". Αγρότης is any kind of farmer, γεωργός is the one that cultivates the earth, not a stock-farmer. So , οι αγρότες είναι οι γεωργοί και οι κτηνοτρόφοι=Farmers are the agriculturalists and the stock-farmers.
How do you know the proper method to change a masculine word to a feminine word? I know that objects are out of the question, but in Spanish you basically just add an a and sometimes drop the last vowel like jefe to jefa. It seems a bit more complicated in Greek.
Nouns in -τής become -τρια.
Nouns in -ης (not -τής) become -ισσα.
Nouns in -ος stay the same mostly.
Nouns in -ας are very very ruleless and may become -ισσα, -ου, -ω etc.
Keep in mind that the "rules" above can be broken, it's just empirical.
Easy to associate the "agr" from agriculture to farmer.
Compare also English "acre".
All ultimately go back to a meaning "field" -- Latin ager "field" > agricultura "field cultivation", Greek αγρός "field" > αγρότης "field-er = farmer".