Interesting, thought provoking questions. I did indeed give it some thought. I suppose that I need to explore my personal definitions of the various type farms mentioned. Please realize that these are my own viewpoints, so someone else may define them a bit differently.
...garden: gardening generally generates no net profit. The gardener utilizes most of the food themselves, though some may be shared or sold. Gardeners aim for pleasure and/or supplementing their livelihood. A common goal is to have some fresh produce for the table.
...hobby farm: usually hobby farms are done for pleasure, and though some are profitable, most do not generate a profit, or should I say a significant net income. Importantly, the goal is not a livable profit. Most hobby farms are part-time affairs often not involving employees. Most hobby farmers have off farm jobs that provide their main income. This is not to say that a hobby farmer isn't serious, nor that they don't contribute to the food system. It's just that if their farm fails to create income or product, they still survive just fine. Another point, most hobby farms are not self supporting homesteads. Operators of these farms still routinely buy their supplies in town. If not retired living off retirement income, most have jobs off farm.
...small farm: small farms are generally profit oriented. Most employ help either from off the farm or via family members. And while many don't always manage to generate a net profit on a regular bases, the attempt and intention is there. Most small farmers don't derive the major part of their food and resources from their farms, but rather look to generate cash via sales. They tend to produce only a few products rather than a wide assortment. Their gross sales are usually below $200,000 (there about) with net profit way far lower. A small farmer may or may not derive significant income via off farm employment.
...homestead farm: unlike other farm classifications, a homestead farm implies that it contains the farmer's residence. It's where the farmer & family live. That's a major difference as far as I'm see it. Hobby and other farmers need not live on their farms. A homestead farmer also aims to produce much of the family resources directly from the farm, primarily food. While outside income may exist, the intent is to live off the farm as much as feasible. It's not profit but rather livelihood that is the aim. But income is still important so as to support the farm family.
My goal is to be able to derive much of my livelihood from the farm, plus income from it's products via sale or barter. And I reside on my farm. My plan is to produce a very wide assortment of foods -- fruits, veggies, grains, livestock. I harvest my own firewood, organic material for mulch/compost/soil amending (a.k.a.- fertilizer), harvest rainwater, use a solar electric system. My trees supply fence posts, building poles, trellises. My rock walls were created using my own rock. I can mine my own volcanic cinder for my needs. Thus this homestead is well along its way to supporting a livelihood for its owners.
Therefore I believe fit my definition of a homestead farm.