No the vax is not a vaccine. Go back before theCDC downgraded the definition of vaccine to include the vax. A vaccine protects against passing on the infection. Without that it is totally worthless to society. The vax provides no protection.
WarpSpeed was admirable, but they lied to DJTrump. He asked for something to protect individuals (mebbe they did that) and society — on the latter they lied. Like a senior manager he gave the order and then walked off leaving the rest in the hands of subs. They got bought and lied.
Like much of the rest of America, he did not know that DC was corrupt.
If you are vaccinated against the Measles and you get the Measles, you can infect someone else because you have the Measles and it is contagious. It’s true of all contagious diseases. It’s why illegal immigration is dangerous. They can bring those diseases into the US.