When Baidu (NASDAQ:BIDU) went public two years ago, investors warmed quickly to the story of Baidu as being China's Google (NASDAQ:GOOG). And why not? Baidu is the high-margin search-engine leader in the world's most populous nation. Shares have rocketed more than tenfold since its $27-per-share IPO.

With all of the untapped upside for Baidu, one has to wonder whether the two may eventually switch places. Instead of referring to Baidu as China's Google, will we one day come to see Google as America's Baidu? 

Well, it's unlikely to happen, for several reasons -- the primary one being that Google is hungry for market-share growth on Baidu's home field.

"We are closing up the gap," Google executive Rebecca Kuei told Reuters this morning.

Third-party data seems to bear that out. Market researcher Analysys International pegs Google's market share at 23% during the second quarter, up from a 19% slice in the previous quarter.

Should Baidu be worried? Is the huge run over? If that's where you're coming from, let me be frank: You're asking the wrong questions, and you're going to arrive at the wrong answers. The only thing that is right is that your assumptions are incomplete.

All the wrong tea leaves in China
Google isn't growing in China at Baidu's expense. In fact, that same Analysys study shows that Baidu's market share has grown to 58% during the second quarter, up from its 57% chunk a quarter earlier.

Google is growing more quickly, but only because it's doing a better job of carving up the 19% of the market that Baidu and Google don't currently watch over in the search space. Among other initiatives, Google has been inking deals with popular Chinese website operators, including SINA (NASDAQ:SINA), Tianya, and China.com parent CDC (NASDAQ:CHINA).

But Baidu is no dummy. It, too, has forged deals with Web-access providers and portals, including Microsoft's (NASDAQ:MSFT) MSN China. It knows how to play this game, the only way it can really be played.

So, yes, Google is technically closing the gap with Baidu. Just don't argue that Baidu is slowing down. After all, go back two years, and you'll find that Google commanded as much as 33% of the search market in China. Where each company stands on the market-share grab depends on where you draw the starting line.

Still, market share is just one component in the growth equation. As the Chinese economy improves, so do disposable income, Web-access usage, and online-advertising budgets. You see the effect in Baidu's own second-quarter numbers, with the company's top and bottom lines more than doubling.

The ultimate upside
I recommended Baidu to Rule Breakers subscribers a year ago at $83.37 a share. The stock has gone on to nearly quadruple since then. It looks great on our scorecard, but that doesn't stop the inflow of new subscribers who head out to our active discussion board and ask the obvious question:

Is it too late to buy Baidu?

It's a fair question. It is repeated often when Baidu's stock crosses round milestones such as $100, $200, and more recently $300.

Growth stocks are going to be risky, and overseas stocks are going to be even riskier. Baidu has certainly come a long way in a short time, but it has done so with sharp corrections along the way. Still, let me make a sobering comparison: Google commands a $180 billion market cap, while Baidu is just an $11 billion company.

Baidu is the top dog in a country that has roughly four times as many people as the United States. Baidu's 58% market share in China is actually greater than the approximately 54% market share that Google is ringing up domestically. With China's economy growing at a better than 10% annualized clip in recent years, it may take decades for China to catch up to our income and consumption levels, but the gap continues to close with every passing year. As China's residents spend more and sponsors spend more to reach them, Baidu's financials will continue to improve dramatically.

Am I suggesting that Baidu's market share will one day lap Google's? No. Those assumptions would also be incomplete. Despite Baidu's recent entry into Japan, its strength in character-based language search does not make it the same kind of global player as Google. In fact, 48% of Google's revenues this past quarter came from its international operations.

Still, it's premature to cap Baidu's potential based on the portrait of China today. The company should be earning substantially more in a few years, even if its market share settles for substantially less. The uncertainty involves why the risks are as wide as the price fluctuations.

However, as long as Baidu keeps busting through Wall Street's profit targets -- the way it has in all but one quarter since going public -- and China keeps taking to the Web, lapping more round milestones is just a matter of time. Maybe Google's aspiring to be the next Baidu wouldn't be a bad ambition after all.

Baidu is a Rule Breakers pick. SINA has been recommended to Stock Advisor subscribers. Microsoft is an Inside Value selection. Why are you missing out on these great stock picks? The answer may be waiting on the other side of a free 30-day pass to any or all of these newsletter services.

Longtime Fool contributor Rick Munarriz has been a fan of China's growth stocks for several years now, even though he does not own shares in any of the companies in this story. He is also part of the Rule Breakers newsletter research team, seeking out tomorrow's ultimate growth stocks a day early. The Fool has a disclosure policy.