Apple Store at Pudong in Shanghai, China. Photo: AP

The new iPhone 4S went on sale Friday. This weekend, Apple sold over four million of them. In three days.That’s half as many units as the best-selling gadget in history (Xbox Kinect) sold in two months.

So obviously, early critics calling Apple’s refresh a disappointment have to feel sheepish. And clearly, customers think the 4S is a pretty attractive phone. But these are surface lessons. What do Apple’s numbers really mean?

Let’s start with the arithmetic. An unlocked baseline model iPhone 4S sells for $650. That’s probably what Apple gets for subsidized devices that retail at $199, too, according to Asymco’s Horace Dediu. So four million devices times $650 equals $2.6 billion in revenue. Since at least a few of those four million were the higher-priced 32GB and 64GB models, we’re probably talking closer to $3 billion in revenue; maybe more if the international pricing of iPhone 4S is more favorable.

That’s more money in a weekend than Google makes from mobile in a year. And that’s not counting iPhone 4s or 3GSes or cases or AppleCare+ or whatever else Apple was able to sell this weekend to people so crazy about the iPhone that they lined up hours in advance, like Soviet-era Russians seeking their daily bread.

Now let’s look at the map. Those four million units come from just seven countries: the U.S., Australia, Canada, France, Germany, Japan and the U.K. Admittedly, those are rich, tech-happy countries whose citizens buy a lot of smartphones, and particularly a lot of iPhones. But on Oct. 28, most of the rest of Europe plus Mexico and Singapore (22 countries in all) join the party. The target is to bring the 4S to more than 70 countries by the end of the year. I don’t think Apple will have a problem selling its next four million 4Ses, pushing past Kinect before the 60 days are up.

Still, Apple’s trouble with the larger map is the absence of carrier subsidies. Customers in most of those countries are paying $650 or more for the 4S, not $199. In the grand scheme of things, this is not a terrible problem to have. There are rich people and aspiring-to-rich people everywhere, and for them, a new iPhone has become a global status symbol. Apple is going to make a lot of money off these people.

But as Apple CEO Tim Cook observed at the 4S launch event, this means that Apple currently accounts for just five percent of the gigantic global handset market. Even if the mobile market is exploding and Apple owns, as it usually does, the high end, there’s still a lid on Apple’s growth, particularly in a sour global economy that’s beginning to really hurt emerging markets. That’s a conundrum for Apple, but also a tremendous opportunity.

There is a huge hunger for inexpensive mobile phones. South Africa has 92.2 mobile subscriptions for every 100 people. Tunisia has 83.3 and Algeria 92.7, against a global average of 60.8. In the global south, mobile phones aren’t displacing landlines but skipping past them. Likewise, even though mobile data infrastructure in much of the world is spotty, smartphones aren’t just augmenting personal computers, but skipping right past them as a primary computing and communications device.

This hunger isn’t just (or even mostly) driven by Apple. It’s fueled the enormous growth of Android, too. But it’s also what’s enabled the fragmentation of Android as a platform. We actually experience Android’s fragmentation in a very minimal way in the U.S., U.K. and North America, because phones’ compatibilities aren’t really so far apart. Globally, the range of hardware and software running Android is enormous, simply because any manufacturer can use it.

Earlier this month, Microsoft’s Andy Lees (head of the Windows Phone division) told me that this variation in price and features is what people frequently don’t understand about the global smartphone market, and specifically Apple’s and Android’s place in it:

On phones specifically, the thing I think is most misunderstood living in the U.S. is just the role of the subsidy and the operator and the price of the device. At the announcement yesterday with Apple, they said “oh, well, we’re down to free [with the iPhone 3GS].” That’s still an expensive phone in the U.S…. Those high prices are paid for in phone contracts.

Even in Europe, there’s sort of an unbundling of the subsidy and the actual data plan. So, data plans can be cheaper in Europe. You know, you can argue that’s good and bad. As a result, there’s a higher smart phone penetration in the United States than there is in Europe, but that means that as soon as you hit a few magic price points, without compromising your end user experience, then your market can explode.

Then you go to places like India, China, and there, the markets are massive, but the price is very sensitive. And it’s the ex-factory price, not the subsidized price, because in India there is no subsidy, and in China, there pretty much is no subsidy as well. So, really, there, there’s a race to get down to cheaper. And that’s why Android has seemingly done okay because they have no rules on what you can run on. So, you can get some very cheap Android phones today. The problem is the experience is random. Sometimes it’s good and sometimes it’s not, and that means it’s fragmented for developers. So, sometimes you buy an Android phone, it doesn’t run a game or whatever. So, it’s unpredictable.

This is why selling iPhones is different from selling iPods and why giving away a smartphone OS is different from giving away a web browser. Apple used to be able to sell iPods to anybody and anywhere for a lot of money, because they were hot-looking gadgets, and Apple didn’t care where the music came from. Google used to be able to give away Android, no strings attached, because Google didn’t really care about the other software that ran on its phones; it wanted to feed into search.

Now, though, Apple and Google have both figured out what Microsoft figured out a long time ago with PCs; you’re not selling a product, whether a gadget or a service, but a platform. This means you need unity and reach, internal coherence and external partnerships. It’s very hard to do; Microsoft in the Wintel era is probably our only real exemplar.

In phones, Microsoft is trying to split the difference between Apple and Android by partnering with Nokia, Samsung and others to sell phones worldwide at a range of prices that can all still run everything on Mango. Google is trying to rein in a bit of that Wild West energy and exert a little more control over the Android platform to standardize it without killing what makes it special — a tough task when you’ve already committed to open source.

And Apple finally has a three smartphone platform at different price points with a genuinely global CDMA/GSM phone at its center (even if it is naturally kept locked down by carriers in the U.S.).

So you can bet Tim Cook is happy to hit record numbers in the first post-Jobs iPhone launch. But you can also bet he has his eyes on the global launches at the end of the month and the month after that. And you can bet that he’s working on a global plan to top this year’s numbers with a new iPhone next year, and again the year after that.