FORTUNE — As soon as Marissa Mayer was tapped to be Yahoo’s CEO, speculation arose that she would bring ideas she learned at Google to Yahoo. But the idea that Mayer will follow the so-called Google model, which centers on search and then extends its tentacles into other territories, is plain nonsense.

Google (GOOG) and Yahoo (YHOO), while similar 10 years ago, are now more unlike than ever before. And Mayer won’t have the time nor the cash to change that.

Her first issue is search. According to data released earlier this month from research firm ComScore, Google’s search market share in the U.S. stood at 66.8% in June, jumping one-tenth of a percentage point from 66.7% in May. Google holds 82.6% of the worldwide search market, according to data from NetMarketShare. In the U.S. last month, Yahoo’s search could only muster 13% market share. And worldwide, Yahoo owns only 6.8% of the search market. That’s a major gap. And not even Mayer, who helped grow Google’s Search into the behemoth that it is today, could change that; Google’s search is simply far too sophisticated to be so easily matched.

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There’s another problem: Yahoo doesn’t actually control its search any longer. Back in 2009, then-Yahoo CEO Carol Bartz signed a search pact that made Microsoft (MSFT) the exclusive “provider for algorithmic and paid search services.” According to a document the companies filed with the Securities and Exchange Commission (SEC), that deal is good for 10 years, and extends from Search to Yahoo’s “applications and other digital properties.”

That agreement ties Mayer’s hands. Her only out would be to prove that the revenue per search Microsoft is generating for Yahoo over a 12-month period is lower than expected. Yahoo has expressed displeasure over Microsoft’s return on its search, saying at a recent earnings call that it was “unable to report progress by Microsoft on closing the gap in marketplace RPS.” The revenue Microsoft is generating through its search is substantially lower than what the companies had set as their goal, Yahoo says.

Still, it’s not clear what Mayer could really do if she pulls out of the deal. Yahoo hasn’t been in the search game for years, and getting back into it is too costly for the ailing company. Yahoo’s only move might be to partner with Google — a decision that would effectively shatter any hopes of Mayer’s company actually becoming a true competitor to the search giant again.

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It may not matter much. Yahoo is an entirely different company than Google. Google has largely stayed out of the content-creation business, deciding instead to leverage information from around the Web. Yahoo, meanwhile, has a host of content properties spanning several industries. If Mayer truly wanted to follow the Google model, she’d eliminate all of those sites. There’s just one problem: she’d lose significant revenue in the process.

And what about advertising? Although Yahoo has a presence in the online advertising market, the company’s market share is on the decline. Back in December, advertising firm ZenithOptimedia reported that Yahoo owned just 8.3% of the online advertising market at the end of 2010. In 2006, the company’s market share stood at 18.7%. Google has watched its share of the global Internet ad business surge from 34.9% in 2006 to 44.1% at the end of 2010.

It’s an even worse story for Yahoo in search ads. According to research firm eMarketer, Google will own 78% of the U.S. search ad market by the end of this year. Yahoo’s share will land at 4.5%. By the end of 2014, it’s expected to fall to 3%, according to eMarketer. Google’s success in the online ad business has been derived from two core elements: search popularity and acquisitions. When more people come to its search engine, Google can generate more cash. It’s simple math. And thanks to that, Google has been able to build up enough cash and equity to acquire major online ad companies, like DoubleClick.

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But Yahoo doesn’t have that luxury. The company recently decided to offload its $7 billion interest in China-based Alibaba just to raise some cash. And with a stock that’s been down nearly 38% over the last five years, Mayer might have a hard time coaxing would-be sellers into a part-cash, part-equity deal.

This isn’t news to Mayer. She undoubtedly knew the mess she was inheriting when she decided to take the Yahoo CEO job and surely has some ideas on what she wants to do. But trying to turn Yahoo into the next Google won’t work. At this point, the companies are simply too different and her operation too diminished to pull it off.