Farm-raised fish are grown in controlled environments or "fish farms". They are usually housed with LOTS (thousands) of other fish and are fed fish pellets (made up of sardines/anchovies, and other small fish). They are also most often treated with antibiotics to treat/prevent the multitude of diseases that can be present when that many fish are in a small area together. Another problem with this is that if the "fish pen" is in open water, it contaminates and causes problems in the surrounding area and the fish/plants that are wild in that area. The meat of farmed fish are also often paler in color and so are often given chemical coloring (canthaxanthin and astaxanthin) to turn their flesh pink and make them more appealing to the eye. They also tend to have higher PCB and dioxin levels and lower Omega 3 concentrations.
Wild-caught fish, on the other hand, eat food from their natural habitat, turning their meat a natural pink color. They also tend to be leaner than their farm-raised variety as they are allowed to swim wherever they want. They usually have lower PCB and mercury levels and are higher Omega 3 (heart healthy essential fatty acids). Basically, more "good" stuff and less "bad" stuff in them!
***Also, I would recommend NEVER buying farm-raised fish from anywhere in China...I've read some disturbing things about them, some of them are summarized HERE. (Read labels - it will tell you where its from - I've mostly seen frozen tilapia and shrimp from China)
Fish can be a great addition to your family's food diet...it is heart and brain-healthy!