Organic farming is a method of sustainable farming, but sustainable farming isn't necessarily required to be organic. As many people know, organic farming does not allow the use of pesticides and chemical agents. It also believes in retaining the ecological health of the land as well as creating as little pollution as possible often using such methods as crop rotation and manure for fertilization. In the US, you must be legally certified to be able to declare your product as organic. However, if you are a farmer that produces less than $5,000 worth of organic products you are not required to certified, but you cannot claim to be certified organic, or us the USDA certified label, or any other such claim.
Sustainable farming seems a much more all encompassing way of life. Sustainable farms are also concerned with the environment but also with how the farms may socially impact the local communities and economically sustaining themselves. Similar to organic farming, sustainable farms will also use such methods as crop rotation and composting, however, if needed they can also use minimal amounts of pesticides. For those raising animals, sustainable farms can adminster anti-biotics to animals if they so choose, whereas organic farmers can not.
In terms of economics, sustainable farmers make an effort to purchase materials and equipment from the small local businesses as well as employing those in the community. Sustainable farms also tend to only sell their product locally, thereby reducing the pollution created by transportation and providing people with a fresher product. Organic produce can be shipped from anywhere.
So, although they are not quite the same thing there are still numerous reasons to support both locally sustainable farms and organic producers. In the end, I personally still believe that the benefits of both of these farming methods, out-weigh the economic benefit in purchasing industrial farmed products. If you're interested in finding out more:
http://www.sustainabletable.org/
I found both of these websites to be quite helpful and full of information. Of course, as always, I encourage you to do your own research and come up with your own conclusions...