$\ce{-}$ in $\ce{NH3-N}$ is just a hyphen, not a chemical bond, with meaning "nitrogen present in form of $\ce{NH3}$ or $\ce{NH4+}$". It can have both qualitative and quantitative meaning.
With rounded molar masses, $\pu{17(18) mg L-1}\text{ of }\ce{NH3(NH4+)} \equiv \pu{14 mg L-1}\text{ of }\ce{NH3-N}$.
Or $\ce{N-NH3}$, AFAIK the convention is not settled.
There can be literally any compound or material instead of $\ce{NH3}$ in the $\ce{X-N}$ syntax, containing $\ce{N}$. $\ce{NO2-N}$, $\ce{NO3-N}$, $\ce{Org-N}$ are very common too, e.g. in context of waste water analysis.
That syntax convention is often used in elemental analysis, where are determined contents of particular forms of nitrogen, recalculated to element content.
The respective molar ratios are the same for ammonia and ammonia nitrogen, as there is 1 nitrogen atom in ammonia molecule. For mass ratios, they have to be multiplied by molar mass ratios.
The topic is related to the more general principle not limited to chemistry: quantities being expressed by an equivalent quantity of something else.
- E.g. spring scales, commonly used on farmer markets, measure an object weight = force. But, they are calibrated in the equivalent mass. So an object with weight $\pu{9.806 N}$ has this weight reported "as mass" $\pu{1 kg}$.
- The content of phosphorus or potassium in solid fertilizers is for historical reasons often reported as $\ce{P2O5}$ and $\ce{K2O}$ content, even if there are no such oxides present. ($\ce{N}$ context is addressed by Nilay Ghosh).