“Pulley” taps were originally designed to tap threads in a pulley assembly. Length was extended, but shank diameter was approximately the same as the thread major diameter.
The shank was used as an alignment guide to reach through the pulley hub. Thread depth could not exceed the thread length of the tap. Today, the term is rarely recognized by recent generations.
“Extension” taps provide additional length for reach just as pulley taps do. However, the shank diameter is reduced to allow tapping beyond the ground thread length of the tap. The shank diameter “clears” the drilled hole.
All this seems pretty straightforward, but somewhere the industry decided to add a twist. In thread diameters 3/8” and smaller,
Pulley and Extension taps use the same Industry-Standard blank. If additional reach is needed, with the desire to tap beyond the thread length of the blank, the terminology changes to Extension/Small Shank.
Above 3/8” in diameter, the standard Extension blank has a smaller shank diameter, and is defined only as “Extension”. When in doubt, specify “small-shank” when tap use is intended to exceed standard thread length.
As with any tool, these extended-reach taps can be made to custom lengths. Most manufacturers have standardized on 6, 8, 10, and 12 inches in blank length (varies by diameter) for stock tools. Maintaining Industry-Standard shank and square dimensions allows the use of standard tool holders.