The basic difference, and this is not scientific nomenclature, is simply the way they grow in nature. Terrestrial orchids, and there are over 200 species, are considered woodland plants, and grow in the soil. The "soil" should be well-draining though. Common species include the cymbidiums, "jewel orchids", and of course the vanilla orchid. Some of these varieties require cold temperatures to initiate their blooming cycle, similar to many "bulb" plants, such as tulips.
Arboreal orchids, the vast majority of the orchid species, grow on trees in nature. They typically are more "warm-natured" and their roots require air for the plants to do well. Soil-like conditions would virtually suffocate their roots, killing the plants. Vanda species for example can grow perfectly fine in a pot or basket, with absolutely no planting media around the plant/roots, or even suspended by some sort of twine, wire, or monofilament.
