Yes, a preferred share may entitle the holder to different parts of the company (see types below).
A Pfd stock is considered a hybrid security because it has similarities to both common stock and bonds. It is called "preferred" because it receives preferential dividend treatment. If the issuer doesn't pay the full amount of Pfd dividends in the prospectus, then it can't pay common shareholders any dividend. It also stands in front of owners of common stock in the event of liquidation though behind bondholders. This isn't likely to matter because in liquidation the odds are that everyone gets nothing.
Like common stock, Pfds represent an ownership stake in the company and therefore they are considered equity on the company's balance sheet. They trade on the stock exchanges but they do not have voting rights.
There are different types of Pfd stocks.
The most common type is a fixed rate cumulative redeemable Pfd stock.
Non cumulative are similar but the dividend is suspended, missed payment(s) do not have to be made up to the owner.
In a Trust Pfd, a company puts its bonds in a trust and creates Pfd shares from it. This accounting gimmick allows the company to deduct interest on the bonds while being treated as equity and making the company appear to have less debt.
Third Party Trust Pfds involve an an entity other than the issuer who buys company bonds and creates a Pfd stock from them.
Lastly, there are a few convertible Pfd stocks (U.S.) which have complicated rules laid out in the prospectus governing conversion into common shares. Prior to conversion, they do not benefit from any increase in common stock dividends but they provide the ability to participate in share price appreciation.