The common cold is a coronavirus.
When you recovered from your first ever common cold, were you immune for all the following years and never got it again?
The common cold is many things. Most often it is a sort of rhinovirus. It is sometimes a type or coronavirus.
You generally become immune to the virus that you have had. But in the case of the common cold, there are many other viruses that can come along and you will not be immune to those.
COVID-19 is a particular coronavirus. The variants appear to be similar enough to the original that immunity to one gives immunity to all.
Comparisons to the common cold do not apply. Broad immunity to the common cold is unlikely. Broad immunity to COVID-19 seems very likely.
If you got other colds, chances are they were either mutated versions of prior viruses, or other different coronaviruses in the general class of “colds”.
Those who were exposed to SARS in 2003 have the antibodies for SARS COVID-19. Yet, some of those who had COVID-19 and took the experimental treatment afterward, have been getting sick with COVID-19 again.
Yes, we are immune from the common cold we caught before. New ones come around, new variants and we become immune to the ones we haven’t experienced before.