"Canonical" in biology refers to idealized or generalized features, for example, in biochemical pathways.
In the description of biochemcal pathways, the term "Canonical Pathway" refers to idealized or generalized pathways conforming to or describing common properties of a particular signaling module or pathway, which may also include "specific pathways", for example, specific to tissues or cell lines, as well as others.
Hence, the term "non-canonical pathways" refers to those that deviate from the canonical paradigm. A non-canonical pathway can also refer to an alternative biogenesis pathway only partially meeting the classical definition and an alternative, less known pathway.
However, canonical and non-canonical pathways may sometimes converge. For example, canonical RNA caps are part of a general common pathway in regulating mRNAs.
In general, canonical in biological research refers to established pathways with common or standard features. When researchers find a new feature in an established pathway that does not fit into the canonical model, it is referred to a non-canonical.
For example, a canonical sequence of DNA, RNA, or amino acids refers to the base or amino acid's most common choice in the sequence at each position.
Ackers & Malgor and Wang et al. review and describe differences between the “canonical Wnt signaling pathway” and the “non-canonical Wnt signaling pathway.” Both reviews describe the non-canonical signaling pathway as the pathway responsible for chronic metabolic diseases, possibly resulting from mutations (see figure 2 in Ackers & Malgor’s publication).
Ackers I, Malgor R. Interrelationship of canonical and non-canonical Wnt signalling pathways in chronic metabolic diseases. Diab Vasc Dis Res. 2018 Jan;15(1):3-13. doi: 10.1177/1479164117738442. Epub 2017 Nov 8. PMID: 29113510; PMCID: PMC5752873. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5752873/
Wang L, Wang H, Duan X, Dai P, Li J. Comprehensive Analysis of the Canonical and Non-canonical Wnt Signaling Pathways in Gastric Cancer. Dig Dis Sci. 2019 Oct;64(10):2830-2842. doi: 10.1007/s10620-019-05606-6. Epub 2019 Apr 17. PMID: 30997579. https://pubmed.ncbi.nlm.nih.gov/30997579/