well they are grown in large corporate farms and for their own family in small family farms
plantations
Private farms are equivalent to family farms or hobby farms that raise and produce animals and/or plants without relying on corporate funding. "Private farms" can be considered farms that don't feel the need to advertise their business to the public, or that are family-owned and run or run by a sole proprietorship. It should be noted though that most farms are not exactly private farms since they are influenced by the public through what the public (being comprised of consumers) chooses to consume that comes off the farm, be it a small family farm, or a large corporate farm.
Still a family farm, despite the size. Here's a fascinating statistic that most don't realize: According to the EPA, 87% of all farms are individually or family-owned and operated. Corporate farms make up 4% of those farms, and only 1% of such corporate farms are solely owned and operated by other-cooperative, estates, trusts, etc. Another source (from the book Compassion by the Pound) states that the number of farms that are corporations themselves are family-owned and operated. Many, if not all such farms started small as the quaint, romantic-type farm many think of today into such large corporations.
If such reasons exist, they are mere misconceptions. Most corporate farms are family farms themselves: it is not possible to replace a family farm with a family farm if it's still going to be a family farm, no matter how large or small it is. The term "corporation" is merely a business label applied to a firm, regardless of what kind of firm or business it is or who it is owned by. A family have just as much right to have their farm labelled as a corporation as any other family owning a non-farming business. To answer the question, many small farms have grown into large farms and have had the corporation label added because of the expressed demand for cheaper and safer food by the consumer. Consumers wield far greater power in the marketplace than the producer could ever dream of having, and as a result the producer is forced to change and adapt to comply with the kind of demands consumers demand.
plantations and large family farms
There is no difference, actually. Many, if not most corporate farms are owned by families, and are still considered a family farm. The term "family farm" should never always equate to a "small farm," nor should the term "corporate farm" should ever equate to a large-scale operation owned by a multi-national company or corporation. Many family farms are very large (often being the largest farming enterprises in the country), and many corporate farms have been formed by families who wished to take advantage of the legal and accounting benefits that comes with operating such a business enterprise.
Monoculture
The plant indigo the people of the southern colonies used is grown on large farms.
Plantations.
It is farm that has had the "corporate" business label added to it due to legal and accounting benefits that the owners wish to take advantage of. It doesn't mean that it's a large operation nor that it is not family-owned; around 98% of all such farms are family-owned and operated.
Fields, storage, where it is harvested
not neccesarily it depend on the way you manage your farm