What makes a double pumper a double pumper?

Vacuum secondaries only open as the engine requires (when properly tuned) and therefore do not require an accelerator pump on the secondary side to help the engine overcome a stumble.

Double pump is generally a term that applies to holleys only. Vacuum secondaries only have one pump and can be identified by the vacuum pot on the side of the carb that opens the secondaries. Mechanical secondary holleys have no vacuum pot and, as stated earlier in this post. Have two accelorator pumps, thus "double pumper", one under each float bowl.