The key difference I've found between a stock split and a stock dividend – of the exact same stock and class, as opposed to a spin-off – seems to be from the company's own accounting perspective. There doesn't appear to be any actual transfer of value to the shareholder with either kind of transaction; i.e. in theory, each transaction would be immaterial to the value of your holdings.
With respect to the company's accounting, a stock split affects the par value of the shares, whereas a stock dividend reduces the retained earnings account in order to increase paid-in or contributed capital.
I found a good online source which explains the history behind this accounting difference:
McGraw-Hill - Intermediate Accounting eBook, 6/e - Chapter 18 - Stock Dividends and Splits.
Besides being based on fallacious reasoning, accounting for stock
dividends by artificially reclassifying “earned” capital as “invested”
capital conflicts with the reporting objective of reporting
shareholders' equity by source. Despite these limitations, this
outdated accounting standard still applies.
REASONS FOR STOCK DIVIDENDS.
Since neither the corporation nor its shareholders apparently benefits
from stock dividends, why do companies declare them?23 Occasionally, a
company tries to give shareholders the illusion that they are
receiving a real dividend.
Another reason is merely to enable the corporation to take advantage
of the accepted accounting practice of capitalizing retained earnings.
Specifically, a company might wish to reduce an existing balance in
retained earnings—otherwise available for cash dividends—so it can
reinvest the earned assets represented by that balance without
carrying a large balance in retained earnings.
There's a lot more on that page, before and after, worth reading.
From another book: Google Books - Comparative Income Taxation, a Structural Analysis - page 314 - Stock Dividends. Small quote:
5.6.2. Stock dividends
The distribution of dividends in the form of stock or "bonus" shares
to existing shareholders typically involves a transfer for corporate
law purposes of retained earnings into stated capital.
It can been [sic] viewed as a deemed distribution of a cash
dividend to the shareholders followed by a corresponding contribution
to capital or as solely as an event at the corporate level which has
no effect on the shareholders whose economic interest in the
corporation is unchanged by the receipt of additional shares. The
systems have taken varied approaches to the stock dividend problem.
The treatment is in part a function of the rules dealing with
distributions of stated capital.
[emphases above are mine]
[... continues w/descriptions of different countries' tax treatments of the kinds of stock dividends. Includes U.S., Sweden, Japan,
Netherlands, Canada, Australia, U.K., France, Germany. ...]
As far as why a corporation might want to capitalize earnings and reduce the equity otherwise available for dividends, I can only imagine that, ignoring taxes for a moment, that it may have something to do with capital ratios that need to be maintained for financing or regulatory purposes? Yet, I remain curious. If I discover more on this then I'll update my answer.