Surely, there is some amount of income that a business’s owner is allowed to pocket without bad intentions, which may or may not come at the cost of long term investments. Especially in stable/declining businesses.
There's at least a clear relationship if the dividend is reinvested.
If the dividend is spent, though, eg by someone in retirement, then they're different. Under buybacks, the retiree would have to sell some shares to get cash, and would eventually run out. Under dividends, the retiree would be able to continuously pocket money.
if the stock goes up 10%, sell 10%. The value you hold is the same.