Historically, large sacks often contained grains; thus the association of these knots with the miller's trade.

[1] Constrictor makes a fiercer binding knot, but Miller's/Bag is suitable for most applications, and is easier to tie/untie.

These fit the short description "two crossing turns – ends tucked under".

The following 3 knots do not fit the simple "two crossing turns – ends tucked under" definition but are very secure: The common aspects of the most common bag knots are two crossing turns, and both ends tucked under some turns near the crossing point.

Two ends, and two turns one can tuck under, gives a limited number of alternatives.