Ammonium (NH4+) is the form of nitrogen that is most readily available to plants. It is produced by the decomposition of organic matter and is also a byproduct of nitrogen fixation, the process by which atmospheric nitrogen is converted into a form that plants can use.
Nitrate (NO3-) is produced by the nitrification of ammonium. It is the most mobile form of nitrogen and is easily leached from the soil. Some plant can use Nitrate directly.