Should also mention things like preferred shares and special voting rights shares.
If I remember Economics 101 from decades ago… Preferred shares are a separate special class of shares guaranteed a certain amount/portion of the profits before the “common” shares see any dividends. Sometimes too, there would be Class A and B shares.
One of the advantages of shares is also - you own X% of the company, you are entitled to an X% vote on members of the Board of Directors and other important issues. The board provides oversight to the CEO who runs the company day-to-day. Usually, major shareholders with say, 20% or more of the company shares, get a big say in who is on the baord of directors. Usually a corporation’s share are so widely held (unless the founder kept a huge chunk) that the corporation is effectively autonomous, self-governing - the executives nominate board members, and unless they’ve really pissed off a lot of shareholders, the shareholders vote for who the CEO/current board recommend.
Sometimes there are separate classes for shares with different voting rights - i.e. these shares get to vote for board of directors etc., these don’t. Or these shares have 10 times the voting power.
It’s all one big circle-jerk. Google any list of board members of any corporation, and they tend to be CEO’s of other corporations, customers and suppliers and big names in the business. Occasionally a figurehead, like a prominent retired politician or celebrity, or a “conscience” vote like a member of a university faculty.
Generally, the board sets the CEO salary and surprise(!) being CEO’s themselves, believe CEO’s in general should be paid enormous amounts of big bucks, irrelevant of performance. The board themselves are also paid pretty good for just showing up and voting at meetings a few times a year.
Also, many higher up executives are paid with stock options - “In 2 years you can buy X stock from the company at today’s price”. So the driving motivation for any executives is to increase the stock price, no matter what it does to the company after those years are up. This also means a company may (many have lately) buy back shares from the market which provides shares for those stock options, and also buying shares can drive up the price… win win. It also means fewer shares out there, and disposes of profits so they don’t have to be handed out to shareholders.
(side note - the difference between stock option price and current market value is considered income for the executive. For example, Elon Musk in 2022 had a $22B stock option windfall for hitting performance targets with Tesla, resulting in a tax bill of $11B, probably the biggest single amount of income tax anyone any time has ever paid. But, he still ended up with $11B in the bank.)
What a company can do with stocks, what information they must disclose, what they can say and whether it’s misleading, stock price manipulation, trading based on inside information the public does not know - all restricted by the SEC to prevent the smaller stock holders from being screwed. You must disclose buying more that 5%(?) of a publicly traded company, and whether you intend to buy out all shares. if so, you must make an offer for all shares to all holdes. You can’t go to company B and say “we’ll buy your shares in Acme and that will give me 50%”