you're thinking about it the right way, and they aren't treated differently the way you're thinking. They way they are treated differently is,

if you just look at historical stock prices you will miss the dividends being siphoned off, so you have to track the dividends and put those amounts back into your charts, and it's mentioned over and over so you don't look at the data and wonder if they did the naive thing or the complex thing.

and dividends are taxed in that calendar year as income at the corporate level, and again at the personal level, and not with lower capital gains tax rates, so the amount left over that is available to the investor to spend or reinvest is smaller than the nominal amount, and taxes change over time, and different income brackets pay different taxes (which is ignored, i think, they just use worst case marginal tax rates) Because dividends are income-taxed, it makes sense to earmark that money to spend on yourself if you're going to be spending any of the money on yourself.

and large "institutions" frequently don't pay income tax (I'm not an expert, but churches, foundations, and perhaps pension funds and corporations which have large losses/expenses/depreciation to write off) but they do play a large role in the investment markets, driving market prices etc.

You know what it all reminds me of? climate science. You can measure a ton of metrics and track them over time and try to predict the future, but the data is only a very rough estimate of what's going on, and the underlying dynamics change a lot over time.