The reason TKN is always is higher than ammonia is related to what the test does. TKN or Total Kjeldahl Nitrogen uses sulfuric acid & catalysts to convert organic nitrogen to ammonia/ammonium. So in the digestion step - we have organic nitrogen such as proteins and amines being converted to ammonium (the digestion step is an acid where ammonia exists as ammonium). The test does not measure nitrate, nitrite, azo groups or nitrogen in ring structures.
Once digested - the sample pH is increased and tested for ammonia. The reading from the sample is total nitrogen. A non-digested sample is also tested for ammonia (using ISE or other ammonia testing method). The non-digested sample gives the ammonia/ammonium concentration.
TKN = total nitrogen (organic nitrogen converted to ammonium in acid digestion step)
Ammonia = increase pH to convert ammonium into ammonia - then read ammonia concentration
TKN - Ammonia = Total Organic Nitrogen (this gives the potential ammonia that can be released as organisms degrade proteins, amines, and other forms of organic nitrogen). Total Organic Nitrogen is abbreviated to TON.
How can a lab have higher ammonia than TKN - it could be error in testing. Or dilution factors required for testing make the error term larger than the difference in TKN/Ammonia - this would require the sample contain mostly ammonia with little organic nitrogen.