bcp, In many countries there is no difference. In Britain anyone with more than a few acres of land that produces something is called a farmer. He might run only cattle, or sheep, or he might grow only cereals, or any combination of stock and crop, he is still called a farmer. Small scale people doing any of that are called smallholders. A big-scale horticulturalist might also be called a farmer by some, but not by others. Growing vegetable and fruit crops for human consumption is usually differentiated there by being referred to as horticulture and not agriculture.
In NSW, Australia, with only 200 acres of cultivation on 3000 I was called a Grazier, or in common terms a "Cockie". I share-farmed up to 2000 acres of cultivation on a neighbouring place and therefore was a Farmer when I worked that land. My agricultural organisation was known as the Farmers and Graziers Association. Real big places in other states sometimes know the bossman only as a Station Owner. I expect they have different names for the same people across Australia.
Here I am Sr. Agricultor. Very polite the Portuguese. An Agricultor is the equivalent of Britain's Farmer - no differentiation on what you produce. No lower limit on the amount of land used either.
As I said in an earlier post, I once checked out several dictionary definitions, and some of them disagreed with each other, so I decided there is no correct definition - it is all in the mind of the individual. From my British roots, my opinion (and only my opinion) is that a Farmer should have some crops and some grazing land. I am quite happy if nobody else agrees with me. It is simply that when I hear the word farm, I think of livestock and crops on the land so described.
We have come a long way from the OP in a short time. If he comes back he will probably give up reading all our chattering.