A Non-Stock Corporation is a Corporation that does not have owners represented by shares of Stock.
A Non-Stock Corporation does not have shareholders.
A Non-Stock Corporation may or may not have members.
Members usually have the same rights, especially the right to vote, as shareholders in a Stock Corporation.
Most Non-Profit Corporations are Non-Stock Corporations because, by definition, the purpose of a Non-Profit Corporation is not to pay shareholder dividends.
In some states For-Profit Corporations owned by only a few persons who have no interest in selling Stock may choose to be a Non-Stock Corporation.
Sometimes a Non-Stock Corporation is formed for a specific short term purpose or
project, for example a construction project.