If you have an CLSC-2000HOB (BH2000) skimmer, then the correct pump is the AQ2000S and not the AQ1000S.
Also, you don't test a skimmer pump for flow. Skimmer pumps are not about the flow, they are about the amount of air that is injected into the water column. The more air the skimmer can inject into the water column per watt, the more efficient and the better the skimmer pump is. So to properly test a skimmer pump, you need to measure the SCFH.
Did you get the wrong skimmer? Not sure, what did you order? If you ordered the CLSC-2000HOB and got the 1000 instead, then yes, you got the wrong skimmer. Hard to tell without knowing exactly what you ordered and what you got.
Can you use the AQ2000S pump on that skimmer. See above.