I am trying to understand the link between the Latin and Greek and the more modern "canon" (or cannon as it seems to be spelled in English) which is a piece of artillery.

The link between the Latin and the Greek is that the Romans borrowed the Greek word. The weapon cannon ultimately comes from the Latin word canna 'tube' with an augmentative suffix, i.e., 'big tube'.

Ceci n'est pas un seing.