This is how I think about it.
Concentration=mass/volume (c=m/v)
In pre-renal azothemia the final mass of urine Na is decreased (due to increased Na reabsorption in the proximal tubules from the low flow of urine, as well as to increased aldosterone due to systemic volume depletion) as well as the volume of urine (due to decreased GFR from the systemic volume loss).
However the urine volume reduction is much greater than the mass reduction, which result in increasing concentration of Na in the urine aka increased osmolarity

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In renal azothemia, or else dysfunctioning kidney, Na cannot be retained and the mass is increasing, and the same is for volume thus reducing the concentration of the urine and the osmolarity.