No, that's not correct. When you buy a share of a publicly traded company (or a private one, for that matter), you are literally buying a fraction of their cash on hand, a fraction of their business operations, a fraction of their trademarks, a fraction of their inventory, and so on. You own part of the company.
The difference with cryptocurrency is that people ditched the entire ownership of anything and replaced it with just a token. It's like if you took a company, hollowed out every single thing that made it valuable, and sold the shares as novelty stock.
Anyone suggesting that stocks are just fun tokens that people trade back and forth doesn't understand what stock actually means. I think this misconception is very popular in the cryptocurrency world because it justifies the existence of tokens and crypto coins that aren't actually backed by anything of value. If you're convinced that nothing matters and it's all just tokens anyway, you're more likely to be persuaded to invest in crypto tokens and shun the stock market.