A hobby farm can have different definitions. But the basic idea is that a hobby farm is a small-scale farm that is primarily for pleasure. The owner or owners of the farm typically have a main source of income, like an off-farm job, a pension or retirement income, or perhaps a trust fund. Whatever the source, the point is that the farm does not have to make money - it can be engaged in on a hobby level.
Hobby farmers may have a lot of money to invest in their farming endeavors, or they may only have a little and be operating on a shoestring budget. But compared to homesteaders, hobby farmers typically aren't driven by the primary goal of self-sufficiency. They may be very content to continue their jobs and farm on the weekends, or to use their retirement income to invest lavishly in the farm animals they choose to keep.
There can be a bit of overlap with homesteaders; it's really a spectrum. A hobby farmer may want to be able to maintain the farm with just a part-time job so that she can spend most of her hours farming. She may also want to have a small budget for investing in farm implements, animals, and infrastructure. In this case, it really depends how the individual farmer identifies. There's a blending of motives and means where a hobby farmer is not very far from a homesteader at times. It's really all about what you feel fits your goals best and describes what you're doing accurately. There are no hard and fast rules.
Learn more about starting your very own hobby farm, and whether it's the right choice for you.