The latest version of the Crane Technical Paper 410 has a great writeup on the definition of these two types of differential pressures:
Orifices, nozzles and venturi are used principally to meter rate of flow. Orifices are also used to restrict flow or to reduce pressure, and are commonly referred to as flow restricting or balancing orifices. For liquid flow, several orifices are sometimes used to reduce pressure in steps so as to avoid cavitation.
Fluid accelerates as it passes through the restriction. The energy for this acceleration is provided by the fluid’s static pressure. The fluid velocity increases and the static pressure decreases until the point of the vena contracta as shown for the orifice plate in the figure below. Fluid velocity then slows and recovers some of the static pressure per the Bernoulli theorem.

Meter Differential Pressure (dP): The difference between the absolute pressures at the upstream and downstream taps (P'1 - P'2) is referred to as the differential pressure, dP, or ΔP.
Pressure Loss (NRPD): The permanent pressure loss or non-recoverable pressure drop (NRPD) is the difference in static pressure between the pressure measured on the upstream side of the primary device before, the influence of the approach impact pressure (approximately one pipe diameter upstream), and that measured on the downstream side of the primary device where the static pressure recovery can be considered completed (approximately six pipe diameter downstream).

So when performing system balancing calculations for pressure drops throughout your system, you will want to apply the NRPD to your system. However if you are taking plant measurements, you will be referring to the metered dP. PIPE-FLO Professional calculates both values, with NRPD listed as simply "dP" and meter dP calculated on the flow meter graph sheet.