Some are weakened live agent. Some are killed or neutralized agent. Some are just a protein or other piece of the pathogen. Some like mRNA vaccines are code from the pathogen that causes your body to generate and then sensitize against something. There are probably other types.
I do find the oversimplification in the debate frustrating. Either all vaccines are bad or all vaccines are great when in reality each one is a different thing. As with other drugs some work better than others and some have side effects while others mostly do not.
As near as I can tell the mRNA COVID vaccine is fairly effective at reducing severity and duration of infection but not nearly so at completely preventing infection. There is a small risk of side effects but the danger from a more severe COVID infection is statistically much greater.
Creating a vaccine in a year is nuts. What we came up with is not half bad given that time frame. We will probably have much better COVID vaccines in a few years.