Statistically most people, vaccinated or non-vaccinated, are not infected. Once infected, both vaccinated or non-vaccinated can transmit if there is sufficiently high viral load. Normally, a high viral load causes symptoms that would cause someone to self-isolate or fail a temperature check, reducing transmission. Because a vaccinated person can be infected without symptoms, there may be some cases where they should be isolating, but are not, and are thus transmitting to anyone, vaccinated or not.
https://www.webmd.com/lung/news/20210729/cdc-reverses-guidan...
> Even if they’re not showing symptoms, fully vaccinated people should “get tested 3-5 days after exposure to someone with suspected or confirmed COVID-19 and wear a mask in public indoor settings for 14 days after exposure or until they receive a negative test result,” the agency’s website says. The CDC previously said fully vaccinated people didn’t need testing after exposure unless they showed symptoms. “Our updated guidance recommends vaccinated people get tested upon exposure regardless of symptoms,” CDC Director Rochelle Walensky, MD, told The New York Times in an email. “Testing is widely available.”
Stanford University will test all students, including those who are vaccinated, https://twitter.com/stanforddaily/status/1425554996683149313
A subset of all populations globally, especially in young people, have already recovered from a Covid variant and have some natural immunity, which is sterilizing immunity (both upper respiratory system--since that is how they got naturally infected--and serum antibodies + T-cells). Governments have the option of performing national sero-surveys to statistically estimate the percentage who are already immune without a vaccine. Individuals who can afford to pay for testing can determine if they have natural immunity, including the newest FDA-EUA test for T-cells (costs $210 with blood draw, only in US for now), https://t-detect.com