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My interpretation (which may be wrong) is a mutation is whenever the virus changes. In a single person the virus may mutate several times. Strains are caused by mutations and are generally considered “strains” when the mutated version starts spreading throughout the population. I think the terms may technically be interchangeable but common language use, all strains are caused by a mutation but not all mutations result in a strain.
Where are you getting the data about so many mutations happening in a single person? This virus has been described as "slow mutating" compared to, say, the flu - or measles.
You are correct that even one point mutation (a change in one letter in the RNA code of the virus) creates a new strain. I posted a picture of the late April phylogeny (family tree of COVID). Due to redundancy in the coding system, most mutations have no effect on the virus's abilities to reproduce or stay stable outside of humans.
Strains spread more rapidly if they have some advantage and the new strain (that is now the dominant strain on the whole planet) is not the strain that first appeared in Wuhan. It may have occurred in southern France or Switzerland or northern Italy, it's not clear yet. Its first known advantage is related to viral load (there are more of the virions in the upper respiratory tract).
IOW, there was a clinical correlation observed (of all the many mutations in COVID, this particular strain actually was causing observable differences in the course of the disease).
If every single person had mutations in COVID inside their own bodies, there would be 77,000,000 different strains of COVID - but there are far fewer than that. If everyone had several (let's say 10) mutations in COVID while they were hosting it, there would be 770,000,000 strains of COVID.
By July, there were about 50 strains (not thousands or millions). I don't know how many there are today and the Scottish geneticists has not yet published any data about the actual point at which the new UK strain mutated. At least, I haven't found it yet, I'll keep looking of course.
You can hover over the little circles (each represents a new strain, with the cumulative mutation locations indicated) here:
auspice
What's not represented is any "UK mutation" except for a couple that, apparently, are closely related to strains from New Zealand (which is fascinating and interesting). The newer South African form (also claimed, without any empirical evidence so far, to be "more transmissible") has a longer history in S.A., but came from Denmark.
So we await publication (from Scotland, from the researcher making this claim about transmissibility) of what the actual mutation is, so we can see from which part of the tree it descended. IOW, this researcher in Scotland (who claims the mutation came from England) must show proof by giving the scientific community the actual mutation points, and the strain (in England) from which it descended. The newest English mutations listed in the nextstrain originally came from a strain in Denmark (so it's of interest that the Scottish researcher has also found the same strain in Denmark, at least that's what MSM says he says).
The fact that mutations occur around the same time as big upticks in COVID can be related to human behavior, and now, we await actual lab studies to see if this single point mutation (in England or Denmark) has led to something more transmissible.