A vaccine doesn't stop a pathogen entering your body, no vaccine...

A vaccine doesn't stop a pathogen entering your body, no vaccine can do that for any virus or disease, it's physically impossible. What it does is arms your immune system with the weapons needed to fight the virus, so it can kill it before you get contagious and before you start showing symptoms (which for COVID is after you become contagious, which is why it's proving so hard to control in the first hand). SARS and MERS (both of which were caused by a different type of coronavirus) were just as deadly, but luckily you weren't contagious until after symptoms appeared so you could control it relatively easily.

So, it stops you from transmitting the virus because your immune system is equipped to kill it before you get contagious, not because it stops you getting it altogether.

Does that make sense?