Neither. The Stock Market wasn't and isn't counted in GDP not is it traditionally part of "The Economy," although it can be taken as an overall indicator of the value of companies and the "mood" of investors at a given moment in a given place. In and of itself the stock market does nothing; hypothetically it could crash all it wants while the economy does well, or can grow as the economy sputters (which is what we've been seeing for nearly a decade). In fact, by mid-1930, the stock market indices had recovered to early 1929 levels, even as the economy was bottoming out.

The true causes of the great depression are still debated among economists. The most widely accepted explanations are Keynesian (still taught in Economics courses today), although I think they place too much emphasis on the nebulous concept of "Panic" rather than concrete market forces. There is also a large "Monetarist" camp which I find equally nebulous.

Rather than the Federal Reserve depressing interest rates like in the 2000's, (primarily) two events stimulated the nine-year bull market in the 1920's; improvements to transatlantic cables allowing 120 words per minute to be transmitted, thus creating global financial markets, and the Great War, which created a large market for foreign debt, which American banks were happy to gobble up. So in the 1920's, American banks were sitting on a mountain of French and British bonds generally considered to be relatively secure. With balance sheets ballooned thanks to "safe" assets in the form of these bonds, between 1918 and 1929 they could easily erogate credit ignoring wobbles in the domestic business cycle, even to those categories which would today be called "Sub-Prime," creating housing bubbles in some regions, notably Florida. Many borrowers defaulted when lenders called in their loans in the winter of 1929-1930, putting additional strain on the banks.

So the October 1929 crash is an indicator; investors had collectively agreed that the US economy couldn't expand anymore. The large fall in stock prices is a convenient starting point for the depression but it certainly didn't cause it, although it sent a strong signal. The US economy had been sputtering for some time; US exports to Europe were declining as European economies which had been wrecked by the Great War got themselves back in shape (it didn't help that tariff wars also discouraged trade) while the the United Kingdom and France were increasingly dependent on reparations payments from Germany to pay the bonds held by American banks; and these reparations payments that were being increasingly paid with loans from US banks, creating cycle of payments that was destined to topple over itself. When panic set in and banks found themselves beset with non-performing loans (both domestically and abroad) plus savers who wanted to withdraw their cash (which the banks had vaporized by lending out) it set off a cycle which was very difficult to break.

In his 1936 "The General Theory of Employment, Interest and Money" Keynes explains that following the dramatic 1929 crash, businesses and consumers revised their expectations "downwards" (i.e. Everything is Terrible). Now, according to "Classical Economics" the fall in consumption because of these revised expectations should lead to a rise in savings (people keep money in the bank instead of going out and spending it) and consequentially, when banks see their balance sheets ballooning with large reserves, they lower interest rates to lend some of that money out; people and businesses see the low rates, take out loans to take advantage of the opportunity, do cool new stuff with the money and revitalize the economy. This didn't happen; Keynes argues the reason is that even with the low rates, businesses were so pessimistic they weren't interested in taking out loans to do stuff. Plus, American banks had been lending at low rates all through the 1920's and lots of people were making purchases, "On Credit." When rates can't go significantly lower, you hit a classic "Liquidity Trap" (similar to what happened in 2007). Lastly, a whole lot of people had invested their savings in the stock market, as over the course of the nine-year Bull market, people became convinced they couldn't lose money.

In his book, Keynes then plugs his own theories stipulating that during economic recessions the Government should step in to stimulate spending and investment. Herbert Hoover had instead increased taxes and tariffs to close the budget defect caused by the economic contraction (not entirely dissimilar to the "Austerity" policies in the Eurozone; less economic activity means there are less things to tax, and the government finds it can't pay for all of its commitments). Franklin D. Roosevelt was one of the early adopters of Keynesian ideas, and the large public works and programs he created, first in New York State during his term as governor, and starting from 1932 as president, are largely credited with having kick-started the American Economy, which returned to its 1929 level in 1935.

In 1963 Milton Friedman would offer a slightly different explanation, postulating that in 1929, as in 1873, 1893, 1901, 1907, and 1920, people's lack of faith in Financial Institutions led them to desire to hold "Cash." Indeed, previous "Financial Crises" had been called "Panics" due to the people's propensity to rush to banks and withdraw their savings lest they lose them. Had the Federal Reserve printed more cash, or simply allowed the printing of cash that didn't have to be backed by assets (notably gold) Friedman argues the fall in consumption could have been averted. However, critics of these ideas say they are overly simplistic, and money supply issues are just as much symptoms as they are causes.