I'll try. I'm no expert but I read a lot about this and people keep asking me to explain it to them. First of all, there is no way to entirely prevent infections and transmission of something that replicates in poorly perfused (low blood flow in the area) upper airways. The immune system works by carrying stuff to infection sites via blood, and so you need enough blood at the place where the virus is before it can be attacked. That's why nobody is claiming total protection from infection and transmission. However, this is highly misleading - the number of replication cycles before immune response stops further spread is
dramatically reduced in a vaccinated person, and therefore both their chances of developing disease, and their chances of passing it on, are severely diminished, and the window of transmission is shortened from days/weeks to hours. So yes, you can theoretically spread it, but once vaccinated you're about as effective at spreading it as a doorknob someone sneezed on, rather than being a walking virus manufacturing factory.
Now, about HIV - HIV is extremely difficult to spread from a single contact (it's got very low virulence) and can be managed very well with treatment, making transmission effectively stop from people in state-of-the-art treatment. However, said treatment is expensive and inconvenient, and has risks of its own, and you need to use it all your life, and it's not available to many people, especially risk groups. By vaccinating people at risk, or large parts of the population, HIV could be eliminated, or dramatically reduced at least, saving the people who would get infected from a life of being medication-dependent, assuming they have access to treatment. So for HIV, a vaccination program won't stop needle sharing and unprotected sex, but will stop people getting even more severe consequences from that. There's a similar vaccination program for hepatitis which has shown excellent results.