There is at least one variant (the Brazilian P.1) that has shown the ability to re-infect people who have already had the disease. There is also some amount of....well, I forget the term, but it's people who get the disease even with the vaccine. In Israel, they showed that of the people with one dose, the variants that people got were largely split between two (I think it was London and South Africa), but once you had two doses, the VAST majority of people who still got COVID got just one variant...and I forget which one it was, but it was one of the two from the pair that predominated for those with one dose.

So, a vaccine doesn't mean you can't get the disease, it just makes it FAR less likely that you will. I don't know whether those who had the disease have the same immunity. There's sound reason to believe that they do not. At least the Pfizer and Moderna vaccines will create antibodies against the spike protein, since that's what the mRNA creates. For people who had the virus, they ended up with antibodies, but what are those antibodies for? The spike protein is the most notable piece of the virus, but is it the only one? A portion of the long haulers appear to have something like autoimmune disease. Could their immune systems have gone after the 'wrong' part of the virus? I don't believe that is known. I'm not sure if that's even a possibility.

As a coder, though, I REALLY like the mRNA vaccines. That's straight up coding there. Those vaccines were being developed to go after a variety of cancers, which even sapator would probably agree are a bit more deadly than the flu. The difficulty is the delivery mechanism, and making the mRNA stable enough to generate proteins. The COVID vaccines show that both of those problems have been solved, so now the same technique can be used to create vaccines against any unique protein target. Certain cancers expose unique proteins, hence the idea of vaccinating against them. It's a pretty interesting thing.