When does one decide to refer to a virus as a new variant?
We use them as synonyms. However, variant is, in my view, more colloquial than scientific. Strains are in the literature often defined by their distinct genome compared to other strains of the same species (might be one base-pair substitution or more). In microbiology, including viruses, we often think of a strain as the proliferation of a single distinct DNA/RNA molecule.
https://www.sciencelearn.org.nz/resources/184-virus-strains