Grass fed means that the cattle were allowed to be fed exclusively grass, hay and forage.
Organic means that the cattle is fed organic feed which could include corn or grain or both, however the cows must have at least some access to a pasture, so at least some of their nutrition will probably come from some grass. The organic cows are not given antibiotics or growth-enhancing hormones.
Grass fed beef have many of the benefits of organic beef, simply as side effects to raising their cattle on a pasture. Because the cows are in their natural habitat, with access to all of the open space you need to support a herd of cattle, their lives are more humane, less stressful, and much more sanitary, which means their immune systems are under less pressure, don’t require artificial assistance, and their meat is much less likely to be contaminated with diseases like E. Coli.
If antibiotics are used on grass-fed cattle, it maybe on some occasion when the animals are actually sick. Cows eat all kinds of plants on the pasture, including weeds, so it would not make sense to spray their pastures full of herbicides however some farmers do and as a result a grassfed non-organic beef may be exposed to more chemicals than organic.
Reading labels before buying your food is always a good thing. You need to decide whether grassfed is more important than organic. Many small farmers cannot afford the organic label however they may be grazing their animals on pasture without chemicals. The only way to find out, is to contact your local farmer.