1. No it doesn't. Pfizer, Moderna both work similarly....they tell your body to create antibodies based on the vaccine's mRNA messages, generally speaking. If you do get infected, the antibody's are lying in wait. One vaccine will not "prevent" anything over the other. Everyone can get COVID, vaccinated or not, and by "get COVID" I'm saying the virus is in your body. Whether that virus is doing anything to you (either asymptomatic or full blown disease) will depend on your immune system....either with the vaccine or without it (some people are just immune).
2. That's misleading. No, the vaccine will not have total prevention of spreading the virus, but it is extremely effective at reducing the likelihood of spreading it by having these antibodys ready to clean up the virus. Less virus in your body means less likelihood of disease and less likelihood of transmission. Some people, whether vaccinated or not, are just screwed. They'll get the disease and have to deal with the symptoms. And those that do are at greater risk of spreading the virus vs those who have had effective results from the vaccination.
I don't know what the percentages are for Pfizer but I'm sure it's similar, they do have very similar mechanisms. I haven't seen any of their data, only Modernas. I'm sure their efficacies are close to each other, the only real difference is their stabilities. No pharma company is going to publish their formulations and methods, but if I had to guess it's probably due to how they deal with Uracil, which is present in RNA and not DNA and results in unstable secondary structures. J&J is and should be much different as it is a DNA vaccine as opposed to a RNA one. It makes sense to me that it would be a single shot, because DNA is far more stable with its tight helix, but it's also less predictable as you have to add another step with RNA production to make the protein. Moderna and Pfizer skip that step.
Just because you have a vector in your body doesn't mean you "have" something. If that was the case, everyone would have flu, some kind of URI, and a couple other infections pretty much 24/7 depending on the time of the year. No medical professional would diagnose you with any virus or infection just because of its presence, and they certainly wouldn't treat you. Once your viral load reaches a point where it overruns your immune system to where you are infectious, symptomatic, or compromised by other vectors that would typically be fought off, then you "have" something. So yes, they do keep you from getting COVID as they prevent your viral load from increasing and they reduce the ability for it to be transmitted to others. At least in the great majority of people. What constitutes "having" something could be debated forever, so just going by how the medical and scientific communities view that.
I get what you are saying with #2, but it's not misleading at all to say that vaccines don't prevent you from spreading the virus. They greatly reduce the chance, but they certainly don't prevent it. If you have had the vaccine, are exposed, and your viral load gets to a point where you have symptoms, you can certainly spread that to others. Thankfully that only happens in a low percentage of individuals.