Although some would argue there is no difference from the standpoint of plant nutrition, the author prefers organic hydroponics to the conventional chemical approach.
The agricultural school professors maintain that plants can't tell and don't care whether the nitrogen they absorb comes from humus composted from old vegetation or animal manure, or from ammonium nitrate spray cooked up in some chemical factory.
I don't believe it. But then, I smile back when melon seedlings grin at me. I do believe that chemical hydroponic nutrients are chemically pure and deliver precisely the nutrients that you pay for. And (as the chemical plant-food makers maintain) that organic nutrients cooked up from some witch's brew of bat manure, kelp, and old crab shells are imprecise and full of impurities. So was St. Augustine before his conversion.
Commercial growers with a tight bottom line will avoid organic hydroponics and stay with the proven cost-efficient chemicals. For now, I'll use both; I'll move to all-organic as I gain more experience.
The primary difference between organic and chemical nutrients (other than the industrial origin of one and the natural origin of the other) is that the chemicals can be immediately absorbed by plants and the organics need a rich, living microflora (many kinds of soil microbes) to break them down into the chemicals that plants can absorb. As we say in organic gardening, we feed the soil and the soil feeds the plants. The makers of organic hydroponics fertilizers are doing their best to grow the microbes and train them to predigest their product, and/or are trying to supply dormant microbes along with the plant food. Experiment and see what works for you.
In time, we hope to produce enough worm casting/compost tea from our indoor kitchen refuse worm-composter (augmented as needed with similar steepings made from garden compost or purchased —chemical concentrates, even, if need be) to feed my hydroponics plantings through the winter growing season. Such an all-natural home-grown "closed system" for growing fresh salads all winter and getting the summer garden off to a month or two head start would be a great step in the self-sustaining program of home food production we're all working toward.