Vaccinated people get in contact with the virus as much as the non vaccinated.
The virus invades the bodies and start multiplying in both populations.
The difference is that the vaccinated body is prepared to immediately attack the virus, something that takes weeks for the unvaccinated body to figure out.
So during the short interval when the vaccinated body hasn't yet wiped out the virus, the person is technically infected, will test positive, and can probably transmit some of the few viruses it has.
But that both vaccinated and unvaccinated can transmit the virus does NOT mean the danger levels are anywhere near similar!
This is probably why so many athletes get positive tests. If you get tested every day, you can get a positive test while a minor infection is defeated, even though you don't feel any symptoms.