From Wickipedia:
"Hydroponics is a method of growing plants using mineral nutrient solutions instead of soil. Terrestrial plants may be grown with their roots in the mineral nutrient solution only or in an inert medium, such as perlite, gravel or Rockwool. A variety of techniques exist."
I would include coir in this.
"The two main types of hydroponics are solution culture and medium culture. Solution culture does not use a solid medium for the roots, just the nutrient solution. The three main types of solution culture are static solution culture, continuous flow solution culture and aeroponics. The medium culture method has a solid medium for the roots and is named for the type of medium, e.g. sand culture, gravel culture or rockwool culture. There are two main variations for each medium, subirrigation and top irrigation. For all techniques, most hydroponic reservoirs are now built of plastic but other materials have been used including concrete, glass, metal, vegetable solids and wood. The containers should exclude light to prevent algae growth in the nutrient solution."
Ok, so, if you're doing the above, you're doing hydro. If you're putting your seed, pre-sprouted or not, into dirt or any of a wide variety of potting soils, you're growing in dirt.
Does that clarify things?