IME, one could make several different distinctions:
- A farming operation which is owned and operated by a singular family, versus one that’s owned by a corporation
- A small*, family-run farm, versus a large farm
*- Small being relative, and probably defined by whatever the person making the argument wants to argue is “too large.”
Twenty years ago, I had ADM (one of the major ag processors) as a client, and I regularly conducted focus group interviews for them among grain farmers across the Midwest: mostly farmers who grew corn/soybeans, but some wheat farmers, too. The corn that they grew was largely used in industrial and food manufacturing uses (corn starch, corn meal, HFCS, ethanol, etc.); it wasn’t sweet corn.
All of the ones with which I spoke were family operations, but one thing to note is that the land which they farmed every year was a mixture of land that they, themselves owned, and land which they leased for the year. In most cases, they were leasing farmland which was privately-owned, usually by a family which used to actually farm that land, but after the family patriarch (and farmer) had passed away, there was no one left in the family who was interested in farming (and often no one left who actually lived in the area), and so, they leased the land out to active farmers.
At that time, most of the farmers to whom indicated that, in order to actually turn a profit growing corn and soybeans**, given the cost of equipment (and other inputs, like seed and fertilizer), a farmer had to be actively farming 1200-1300 acres, at a minimum, across the various tracts of land that they had under their use. That minimum number may well be higher now.
I would still consider those to be “family farms,” despite the relatively large amount of acreage that they farmed; YMMV. On the other hand, it may be that my “data” is out of date, and corn/soybean farming is now largely the province of actual corporations.
**- For those who are unaware, it’s typical for corn farmers to rotate crops between corn and soybeans; corn requires nitrogen it grows, while soybeans are “nitrogen-fixing,” pulling nitrogen from the atmosphere, and “fixing” it back into the soil through its roots. This crop rotation reduces the need for nitrogen fertilizer for growing corn.