Are the COVID vaccines substantially different from/inferior to other vaccines in terms of their effectiveness?

The issue raised, and I’m mostly paraphrasing here, is this: Most vaccines (e.g. measles, smallpox) have efficacy defined such that (for example) a 95% effective vaccine means that for a group of thoroulghly exposed people, 95% of the vaccinated are “immune” and will not get infected or pass the disease along and 5% might. The protection from infection is all or nothing and whether one can transmit the disease is also all or nothing (the “infected” can, the “not infected” cannot). That’s why they don’t have resurgences and “breakthrough infections” for most vaccines.

The COVID vaccine is fundamentally qualitatively different from other vaccines in that neither the “immune” nor “unprotected” states of the vaccinated are absolute; the vaccines will not prevent people from getting infected or spreading the disease. And that’s why there are breakthrough infections and resurgences of the disease even in heavily vaccinated populations. The example of a similar “different” type of vaccine that isn’t “effective” and doesn’t provide “immunity” is the flu vaccine. The measles and smallpox vaccines are of the “normal”/effective type.

The CDC was provided as a source for the claim/definitions: “Historically, the vaccine has been effective in preventing smallpox infection in 95% of those vaccinated”

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