How is this "jab" supposed to "slow" or "prevent" other people from getting Covid-19 from you?

I generally understand that it may help reduce symptoms, but have no idea what else these injections will do to "slow" or "prevent" an jabbed individual from infecting another?

Assuming the jab you got is for the strain going around - does it prevent you from spreading it?

People are saying it does prevent the spread.

What exactly are they basing this on?

How plausible or probable is their explanation?

I want to understand this better from both sides - even if you disagree with the other side. I haven't been able to articulate this yet, and hearing a concise take on this would be useful.

I'm guessing this is all they have - if so - how strong is this argument is. Is there any compelling evidence in this particular study? I keep hearing that a vaxed person can still infect another - but if this is correct below, then it would be less likely - or maybe it's not related at all.. Thoughts?:

"Other study findings suggest that fully or partially vaccinated people who got COVID-19 might be less likely to spread the virus to others. For example, fully or partially vaccinated study participants had 40 percent less detectable virus in their nose (i.e., a lower viral load), and the virus was detected for six fewer days (i.e., viral shedding) compared to those who were unvaccinated when infected. In addition, people who were partially or fully vaccinated were 66 percent less likely to test positive for SARS-CoV-2 infection for more than one week compared to those who were unvaccinated. While these indicators are not a direct measure of a person’s ability to spread the virus, they have been correlated with reduced spread of other viruses, such as varicella and influenza." https://www.cdc.gov/media/releases/2021/p0607-mrna-reduce-risks.html