>Id understand it if the vaccine was a newer version that is better adapted to recent mutations but apparently it's the same stuff we already had a year ago.
That is indeed not immediately obvious, but here is my understanding:
A version adapted to a new variant would indeed be better. It takes some time to develop, but it can be done very quickly. Only a few days or weeks and I think they're already done. Then they need to go through testing and official authorization again, which is a couple of months and then they need to get production going. It will be about half a year until this is available to basically everyone. As far as I understand they considered doing this for the Delta variant, but determined the original version was still good enough and didn't bother. For Omicron it will probably be done, but it will not be here quickly enough for the current wave. Maybe an Omicron booster will be available next year.
Now, why do they recommend boosters?
Your immune system reacts to vaccines and illnesses by producing antibodies. They float around in your blood and can immediately attack the viruses. Virus comes in your nose, antibody kills it. When no viruses come in, the antibodies go away again. Now viruses can come in and multiply before the body produces antibodies again. If you were sick previously or are vaxxed, this production of antibodies will be quicker than the first time you encounter the virus. But it still needs some time to produce the antibodies again and in that time you might get mildly sick or even spread the disease around for a few days.
If you're vaxxed two times a while ago, your body already knows how to produce antibodies, even if you don't have any anymore. When you encounter the virus, your body can react and you will most likely not die or go to the hospital. But you are still likely to get sick.
If you're recently boostered, you have antibodies and you will kill the virus much quicker. You won't get as sick and you won't spread as much.
Is that understandable at all?