Viruses have mutations all the time in random places in their genome, in fact in the course of an infection you have a "quasispecies" of viruses in your body with a diversity of different genomes, but most of those mutations don't do anything relevant. Think of someone modifying a // comment in your code or adding/removing an empty if clause somewhere. In some viruses, mutation is very relevant to fighting the disease, e.g. for HIV it's immensely large. But for the Coronavirus the mutation rate is rather low, and even though it does mutate, no variant has been discovered yet that's functionally different to already existing variants.
The main reason for why Coronaviruses don't mutate much is because they don't have to. While influenza constantly comes up with mutations so that it can come back seasonally, it seems that Coronaviruses take a different approach by evading adaptive immunity instead. E.g. feline Coronaviruses can infect cats over and over again, without large increases in ability for cats to fight it. That's also the case a bit for SARS-Cov-2, there are reports of humans getting infected a second time, but they are rather rare reports, we'd have far more of them if humans had no good adaptive immunity.
One thing to be careful about is using a influenza as reference. Influenza is a segmented virus. The viral genome is composed of 8 separate segments. In the wild new strains occur due to reassortment where the RNA sequences from two separate strains are shuffled to produce a third. That makes influenza annoying because it's regularly swapping in RNA segments from bird and swine influenza viruses. Makes developing an universal vaccine impossible and occasionally you get nasty novel strains like in 1918.
Viruses don’t mutate?