Its kind of just really semantics, people that deal in evolutionary biology get all technical about what they consider the definition of strain and variant and such. So it gets complicated when people are like X amount of mutations means its a new strain while less is a new variant, where others define it based off of functionality, so if there is a phenotypic change to the virus then its a new strain as opposed to a new variant. If you use the later definition then you technically could call something like the Covid-19 South African variant a new Covid-19 strain as its change the phenotypic aspect of the virus.
If you use the simplistic definition that Covid-19 is a coronavirus strain from the coronavirus family in the idea of SARS, MERS, SARS-Cov2 are strains, and then anything varying in enough mutations from the original Covid-19 strain is a Covid-19 variant, then its simply its harder for a coronavirus to mutate than a flu virus. Coronaviruses have proofreading RNA to fix mutations, slower mutation rate, and are single stranded. Flu virus is segmented meaning large segments can be exchanged between strains/small segments can incorporate so more variation.
TL/DR: Coronavirus is more stable than flu, the definition of variant and strain is just made up, Flu circulates with what could be considered almost different species, Flu A, Flu B, etc.., would be like if SARS-Cov-2 was circulating with MERS, SARS and you wanted a vaccine to prevent all of them.
