Not quite. As far as the terminology goes, I don't
think they're the same, since to me having disease implies feeling ill—note "disease" = "not at
ease" = "COVID-19"—whereas infection implies merely carrying the SARS-CoV-2 virus in your body regardless of any visible effects. (Having SARS-CoV-2 does
not imply you have COVID-19!) But in any case, let me clarify this.
What I agree with (and in my initial comment I said nothing about) is that it matters if people can spread the virus to others.
What I don't with is that it matters if you're "infected" if you can't spread it to others (and don't have severe symptoms).
The important thing here is that, from what I recall Dr. Fauci said a month or so ago, there have been promising indications that vaccinated people who get infected with the virus are both significantly less likely to get the disease (COVID-19) and to transmit the virus (SARS-CoV-2) to others (independently of the disease, COVID-19). You can read about this on the CDC website [1]. (And my assumption was that was a big factor in why they lifted the mask mandate... because fewer people are capable of spreading it even if they get the virus.)
So no, it doesn't matter if you merely get infected. What really matters is how many people can become severely sick as a result of your infection, whether that's you or others. Which is important because these vaccines seem to limit transmission itself.
[1] https://www.cdc.gov/coronavirus/2019-ncov/science/science-br...