The main reason for the discrepancies is that state and county data, which the C.D.C. relies on to compile its statistics, does not always properly link the record of people’s booster shots to the records of their initial vaccinations. When the two are not connected, the booster is recorded as though it were a first dose given to a previously unvaccinated person.

This can happen when people go to a different location for a booster shot than they did for their original series of injections. That often occurs when people move, or the place they received their first doses doesn’t exist anymore, as is the case with many government-sponsored mass vaccination sites that closed after a few months. Sometimes a different location for a booster is chosen simply because it’s more convenient.

Data reported to the C.D.C. is stripped of personal information, which makes it difficult to spot and correct these sorts of errors.