This is best explained through an example.
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Let's say it's 6 PM ET, the market is closed, and Google ended the previous day at $100 per share.
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Moe enters a market order in dollars for $100, while Leila enters a market order in shares for 1 share.
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The next morning, the stock price opens at $110 per share. (The U.S. markets have after-hours and pre-market trading sessions that can affect the share price available to Raseed's prime users.)
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Both Moe and Leila's trades are executed at 9:30 AM ET.
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Moe receives 0.909091 shares for his $100, while Leila gets 1 share for her $110.

That's the difference between the two market order types!