To spell it out, ignoring transaction costs and taxes the following two are economically equivalent:

- You own some stock. The company pays dividends. You reinvest the dividends into buying more stock.

- You own some stock. The company buys back stock.

A different equivalence:

- You own some stock. The company pays dividends.

- You own some stock. The company buys back stock. You sell stock until your percentage share in the company is the same as before.