What is the difference between paying back shareholders a dollar amount each year vs paying them a dividend? Is it the same thing?
If you keep your shares and the company pays shareholders a certain amount per share, that's probably a dividend (see comments). In the US you'll receive a 1099-DIV for tax purposes.
In some cases, like a privately held company in which you hold shares, you could receive Capital Distributions instead of dividends and will get a Schedule K-1 for tax purposes.
If you have shares and someone pays you for them and you don't keep your shares after the transaction is over, it's a stock sale. There's a 1099 for that, too.
If you never had any shares to begin with and you gave a company money and they pay you back with interest, it's a loan. You should receive a 1099-INT.