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.
Variants of the common cold?
Is not the current scare, variants of Corona Virus 19?
This pandemic is along the lines of 2009's H1N1 (which is still around) though the Left did not know how to us it to their advantage.
They learned from '09...
Pandemic
Lock down
Present a patsy as a candidate
Steal a election
Free money to those that stay home
Move to socialsm
Pandemic II
Then...?