I would encourage people to think much more broadly about this. I discuss this issue with people all the time. I call myself a farmer to most people. Yet, I only work 10 acres part time. Here is some of my thinking on this.
For those who think scale is the determining factor, I point to herb farms that make $100,000s annually all confined within a
greenhouse in the middle of an urban center.
For those who think crop is the determining factor, I point to fish farms which are lucrative farming.
For those who think cultivating the
land is the determining factor, I point to commercial
mushroom operations in
concrete bunkers and
poop racks which seems more about being an HVAC technician than anything else. They are farms.
For those who think economic return is the determining factor, I point to many row crop farms that end in the red without a net income for the farmer, but they are still considered farms.
For those who think the amount of time spent on the operation is the determining factor, I point to truffle farmers who harvest that strange fungus while on a pleasant walk with a dog or pig.
For those who think primary occupation of the farmer that is the determining factor, I point to many farmers who have town jobs and work their farming activities around that.
I could go on, but I think my point is made. All of these examples are farms. So, I would simply let the person self-designate what and who they are regardless of their practice, crop or growing medium.
Now, if we're talking about a government classification, there is some definition of that in each state and each federal government. However, in Missouri, my 10-acre place that I only work part time was assigned a "farm number" last year.
If someone prefers to call themselves a farmer or a gardener and they plant an acre of sweet corn and
sell it out of their trunk on the side of the road, I say "right on, brutha!"