No, that doesn't answer the question.
In fact, it does.
Why would there be any difference? I mean the vaccination works or it doesn't. If it doesn't work; then one vaccinated person could carry the disease, and spread it to another vaccinated person.
No, you are mistaken that "the vaccination works or it doesn't". It is not absolute, I'm surprised you haven't heard that it is something like %95 effective, meaning both that with some few people, generally those with compromised immune systems, it will not work and with most everyone it will be at least partially effective, meaning if they do get infected, it will be less serious.
Furthermore, the amount of viral load a person is exposed to affects how seriously he gets infected. The greater the load, the worse the infection is likely to be, which is why younger, healthier doctors and nurses who got heavily exposed were more likely to die than those who had light exposure.
If it does work; then why would it matter whether or not a vaccinated person was exposed to someone, vaccinated, or unvaccinated, who was carrying the virus?
Again, it is mostly effective, but not entirely. It is not all or nothing.
Fire burns, right? A raging fire burns hotter and more completely than a mere spark, yet a spark can lead to a bigger fire under the right conditions. Wearing masks where a spark can trigger a major fire is a preventative - not perfect.
So in other words, behind closed doors he's taking unnecessary risks; but out in public he puts on a good show; while he tries to tell others how to live their lives?
No, he is following the CDC recommendations while trying to get people to do the same.