First, it's important to distinguish between genotype and phenotype. Most genetic mutations don't cause any change in behavior or appearance, so the two individuals are phenotypically equal.

With sexual reproduction, individuals can differ genetically but still be compatible, so there is some notion of a pool with a clear boundary. For viruses, this is of course a bit trickier because they "reproduce asexually"[0] and quite rapidly, so mutations happen at a high rate. But one useful property to distinguish them is which receptors (and thus which cells) they bind to, generally affecting what symptoms and diseases they cause.

[0]: Viruses are not considered living things, so the concept of reproduction is already quite a stretch.

> With sexual reproduction, individuals can differ genetically but still be compatible, so there is some notion of a pool with a clear boundary.

The boundary isn't very clear.

https://en.wikipedia.org/wiki/Ring_species

A can breed with B, B can breed with C, C can breed with D, and D can breed with A.

But A cannot breed with C.

Are A and C part of the same species, or not? These "ring species" occur around geographic rings, such as the Arctic Circle, so each population remains genetically compatible with its neighbors... but not "across the ring".

https://upload.wikimedia.org/wikipedia/commons/thumb/8/8d/Ri...

Yeah. Basically the concept of species is bust taxonomically and largely a social construct at this point. (That is to say, what is a species is what the community agrees to be a species for the sake of convenience)

> so there is some notion of a pool with a clear boundary.

That's a model that kind of works most of the times, but not always: the most known example are Bisons and Cows which can breed together and the offsprings are fertile : https://en.m.wikipedia.org/wiki/Beefalo

In fact, most of today's bisons have cows' genes in their genome.

Current scientific literature suggests that viruses change by small amounts all the time, and every now again (3-5 years for influenza) there is big 'jump' in which a significantly novel strain is identified and characterised. See this excellent review for further explanation:

The evolution of seasonal influenza viruses - Velislava N. Petrova & Colin A. Russell

https://www.nature.com/articles/nrmicro.2017.118

I think usually the gene name isn't changed. For example, I've noticed that bacterial genomes tend to start with the dnaA gene (many different sequences).

I like to think of genes as their amino acid or dna sequence only, and internally whenever I need to manage a ton of sequences their names are just hashes of those sequences.

Well, genomic data is objectively discrete rather than continuous. And even if you really wanted to approach it as "continuums", what dimensions could you possibly use?

Perhaps you mean to say that strains should be defined in a fuzzy manner? If so, from my very limited knowledge of systematics, they already are.

It's discrete just like info that one has 19001.18 bucks in their account rather than 19000. Precise yes, useful not very.

I guess ‘behavior and appearance’, mentioned in another comment, are the more practical dimensions, but I still wonder how useful the distinctions are.