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they are not same because vaccinated are less likely to be infected and hence less likely to spread disease.

every vaccinated person is 40% less likely of getting infected compared to unvaccinated. so if a person goes to office with vaccine mandate, they are 64% less likely of getting infected compared to no vaccine mandate.

That very well could be balanced out somewhat by vaccinated people being less careful than non-vaccinated, and possibly by them being more likely to be asymptomatic (but still spreaders).

This does not take into account the delta variant, and also viral load levels.

I’m not sure why you’re downvoted, this is an accurate depiction. The vaccine does not prevent infection/transmission, despite lay people commonly believing it does.

Link please?

https://nypost.com/2021/07/20/white-house-aide-nancy-pelosi-...

"The overall vaccine effectiveness against transmission was 88.5%." https://www.medrxiv.org/content/10.1101/2021.07.13.21260393v...

This of course, does not include the new and improved delta variant.