You are correct and probably incorrect.
There is no “common cold”. Rather there are I believe numerous rino viruses that produce the symptoms. Thus although perhaps several vaccines against specific rino viruses could be cooked up, there would still be others .
The Covid 19 virus is specific.
There are already vaccines against Covid 19 created in very recent time. The vaccines must be tested before being released. That process is tie consuming.
There was a thread describing work by a San Diego lab that made a vaccine in three days after receiving the Covid 19 genome. There are reports her of 14 different vaccines apparently now existing.
So based on what I have read here, the problem is testing and approval and then manufacturing
The Covid 19 virus is specific.
It is already mutating out in the wild. There appear to be multiple strains, and some are milder or deadlier than others.
Influenza is a better example than the cold, and I already mentioned its many mutations that require new vaccines every year.
However, my point was not to downplay a potential vaccine, but to argue against remaining in any deep lockdown awaiting a vaccine.
It could be a long wait, or not be as effective due to mutations.