Here is a starting point: the Science Signaling journal have a definition here:http://stke.sciencemag.org/about/help/cm.dtl
"Canonical Pathways" -- idealized or generalized pathways that represent common properties of a particular signaling module or pathway..." they also define "specific pathways" as those specific of tissues, cell lines, etc.
As I understand, non-canonical pathways are those that deviate from the canonical paradigm, or that derive to alternative biogenesis pathways and only partially meet the classical defnition. Sometimes non-canonical pathways are those which are alternative less known pathways.
Canonical and non-canonical pathways may be semi-redundant, which means that there may be process(es) where these pathways converge.
Souce: NovoPro 2018-04-03