Here's an overview:
Point One: For a private company (not one that is publicly listed on a stock exchange) or public company (one that is publicly listed on an exchange), one can own a share of it. That means a percentage. For a publicly listed company, a person could also own some percentage of a company. For example, you might own 10,000 shares in a company, and that could represent some percentage of the total number of shares. For example: a 2% share in the company. In that sense, share is uncountable. it means a percentage of ownership of the overall company. This use of share is often expressed as owning a 2% stake in a company. share, equity stake or equity share of a company are all the same thing.
Definition: equity stake, which is also called a share
Point Two: Now, in addition to the meaning that indicates percentage (to own a share of the company), you also own shares in a company. The shares (countable) are the units with value that you own. In a private, or privately held company, the owners decide what a share is worth; for public companies, the market decides what a share is worth. Listed shares also have a nominal value that is the value for a share on the books of the company.
Point Three: Companies are said to issue stock (the actual paper with the nominal value of the company on it; today, this is often virtual stock though paper stock certificates still exist).
Difference between stocks and shares:
"For example, "stock" is a general term used to describe the ownership certificates of any company, and "shares" refers to the ownership certificates of a particular company. So, if investors say they own stocks, they are generally referring to their overall ownership in one or more companies. Technically, if someone says that they own shares - the question then becomes - shares in what company?
Bottom line, stocks and shares are the same thing. The minor distinction between stocks and shares is usually overlooked, and it has more to do with syntax than financial or legal accuracy."
Read more: What's the difference between shares and stocks? | Investopedia difference between stocks and shares.
In general, the explanation above holds true for AmE and BrE.
Also, in general, I would ask you: How many IBM shares do you own?
I would ****not**** say: How many IBM stocks do you own?
Similarly, I would say: I don't own any stocks or bonds
I probably would not say: I don't own any shares or bonds.
However, I might say: He sold most of his IBM stock.
Used to mean all the shares he owned in IBM.
Point One: Definition: shares, nominal value and market value and general definition
Point Two: Definition: privately held company