[morelisp]

> Somewhat annoyingly there is no common thread to their meanings

The common thread is the Latin word "norma" for a carpentry square. This gets taken literally in cases like "normal vector", figuratively in cases like "Euclidean norm" (i.e. to measure) then increasingly distant as the word is a root to mean usual/ordinary/average (i.e. according to standard measure) in many languages and thereby ends up in "normal number", "normalized vector", etc. "Normal distribution" inherits it doubly, Gauss used it in the orthogonality sense and later authors in the ordinary sense.