Ammonia and ammonium are two of several forms of nitrogen. Ammonia is released by fish and some bacteria but the pH of the water determines the actual form according to the ions. Ammonia is also influenced by temperature as well as ionic strength. The more acidic (lower pH) the water, the more prevalent ammonium is over ammonia, and in reverse the higher the pH above 7 (more basic) the more ammonia predominates. Ammonia (NH3) is harmful to aquatic organisms, while ionized ammonium (NH4) is basically harmless.
That is why those of us with acidic aquaria (pH in the range of 4 to 6's) never have to worry about ammonia. Most aquatic plants also take up ammonium as their preferred source of nitrogen.