Read the papers on it, antibody tests in people who have previously tested positive for covid have found little or no antibodies in tests taken 3 months after infection. So it appears as if there is a limited/short term immunity after initial infection. The vaccine appears to produce a much stronger immune response, such that antibodies can be identified in tests some time after the vaccination.

You can get limited immunity from the common cold after being infected but you are just as likely to catch it 12 months later anyway. With covid that means we are dealing with it annually, which our health services cannot keep up with.