Jim,
It is difficult for me to research this topic without access to the actual parts, but let me start with some terminology:
What NAPA calls a 'continuous duty' solenoid is one that can sustain a constant current through its field windings to keep it pulled in. An 'ignition type' solenoid would be one that is not continuous duty, meant to switch a high current for a short period of time -- like the starter motor on an engine. By contrast, a "latching relay" does not need a steady application of power to its field winding to maintain a switched condition, and can be pulsed into either the ON or OFF state where it remains until the next control voltage pulse.
I suspect the solenoid you got from NAPA looks much like the first image below. The Intelletic is shown in the second image, the KiB in the third, and Cole Hersee in the fourth image. Which one is most like the relay you took out that was the original part???
Chuck
NAPA solenoid.jpg