No. Members of the public can own stock. The public does not own stock.
> You have bought a Ferrari, so you own it.
No. I have not purchased a Ferrari, so I do not own one.
> https://en.wikipedia.org/wiki/Public_company
This link does not talk about public ownership.
> https://en.wikipedia.org/wiki/Public_sector
This link talks about public ownership in the same way I have explained.
You are not the public. You are a member of the public.