You can argue that cash dividend is a kind of split as well by this logic. The stock price on ex-dividend gets a hit coincidental with the dividend to be paid, so one can argue that the investor has the same cash value on the day the dividend was paid as if it wouldn't be paid at all.
However, for the company to distribute stocks instead of cash may be advantageous if they have low cash reserves but significant amount of treasury stocks, and the stocks are of high liquidity.
It is also a way for the company to release treasury stocks without diluting the current shareholders and creating taxable income to the company, that's an important factor to consider.
This is in fact the real answer to your question. The main difference between split and stock dividend is that in split, the stock distributions proportions don't change.
With stock dividend - they do. While the outstanding share proportions do not change, total proportions do, because of the treasury stocks being distributed. So company has less stocks in its vaults, but everyone else still has the same proportions of ownership. Compare this to split: company's treasury stocks would be split as well, and it would continue essentially sitting on the same proportion of stocks.
That shift of treasury stocks to the outside shareholders - this is what makes it a dividend.