What's the difference between "the third day running" and "three days running"? [closed]

Their meanings seem the same. Are there any difference between them?

India's Prime Minister Narendra Modi has Urged Hindus not together for a major religious festival as the country continues to register record numbers of coronavirus cases.【Infections are at an all-time high for the third day running with 234,000 new cases.】

Could " the third day running" in this sentence be replaced by "three days running"?

"Infections are at an all-time high for the third day running with 234,000 new cases."
Could " the third day running" in this sentence be replaced by "three days running"?

Not really. The case total given refers only to the third day, not to each of the last three days. Three days running usually refers to three consecutive days in a continuous sense. The third day running focuses on the last of three consecutive days and evokes a day-by-day, as opposed to continuous, sense of time. Since the case counts are daily tallies, you want to be able to bin* the tallies day by day.

It's been raining for three days running. We had an inch of rain today for the third day running.

*breaking up a continuous stream of events into sets of hourly, daily or weekly totals is called binning.