Ordinary shares are by far the most common form of equity security.
Ordinary shares are equal to other ordinary shares in both entitlement to share in profits and in voting rights.
Some companies have other classes of share with greater or less entitlements. These include non-voting shares or shares with extra voting rights. These are disliked by investors and are becoming less common.
The combination of entitlement to a share of the profits and a share of control of a company, means ordinary shareholders are the owners of a company. There may also be other classes of shares with similar rights.