As long as the thing that calls itself a “share” is correctly named, then it is by definition a security. All true shares are securities. To see why this is so, let us look at definitions of these two terms.
A share can be defined as a unit of ownership of a debt, a company, or other investment. In other words, any of these things can be split up into any number pieces. The pieces of the company (or the debt, the mutual fund, or whatever) can then be sold to individual investors. These pieces can easily be traded between investors.
A security can be defined as any proof of ownership that can be easily traded. A security is simply proof that you own an asset. It can be, for example, a bond that shows that you own part of a company’s or a government’s debt. It can also be a stock, which shows that you own part of a company. If a share is a unit of ownership and a security is proof of ownership that can be easily traded, then clearly something that is a share is also a security. It is a piece of a financial asset that you own and that you can easily trade.