From page 9 of their manual - EXPLANATION OF TWO OF THE MORE COMMON CHUCKING TECHNIQUES USED IN THIS MANUAL
http://www.teknatool.com/products/chuck_accessories/General/downloads/Accessory%20Jaw%20Manual_Nov07.pdf

SPIGOT OPERATION
Contraction of the jaws around a wooden spigot for grip. Mainly used for box,
goblet and vase turning, that is, endgrain items with a fair degree of overhang.
Generally tailstock support is minimal or cannot be used because of the need to
hollow out the inside. This method seems to be preferred by many bowl turners
over the internal dovetail recess as the foot can later be re-shaped or removed, if
desired, to make a smooth outside bottom of the bowl.

So, in my interpretation of Teknatool’s statement, a “spigot” is always endgrain, AND unsupported at the tailstock when they are talking about capacity. Certainly I do not think they mean that you can not use them to turn a softball bat (supported at one end) or turn a larger diameter with tailstock support. They also give much different dimensions for bowls using “expanding dovetail” method for the same jaws.

It seems to me that in woodturning this method is either spigot or tenon. However, I have never seen a flat worker make a tenon (as in mortise & tenon) cross grain.