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Steve Jobs at the iPad 2 unveiling. (Credit: Apple webcast.)

To understand the competitive mindset of Steve Jobs at any given moment, it’s important to listen to the sales updates that the Apple CEO traditionally gives at the beginning of the company’s special events. But it’s not the numbers that matter so much as the rivals they put in the crosshairs.

And it’s no coincidence that Amazon.com was Topic No. 1 at the iPad 2 unveiling last week.

After announcing 100 million book downloads for the Apple iBookstore, and trumpeting a deal with Random House, Jobs (back temporarily from his medical leave) turned to the topic of online commerce — telling the crowd that the Apple ID logins had reached an important milestone.

“Recently we just crossed 200 million accounts,” Jobs told the crowd. “These are accounts with credit cards and 1-click purchasing,” he said. “Now, Amazon doesn’t publish their numbers, but it’s very likely this is the most accounts with credit cards anywhere on the Internet.”

The relationship between the companies has historically been cordial. Apple was actually the first company to license Amazon’s controversial 1-click purchasing technology, which explains why Jobs was able to use the phrase last week without fear of legal repercussion. But that was back in 2000, and in recent months the two companies have increasingly been crossing paths, and swords.

Last month, Apple’s rollout of in-app iOS subscriptions — giving itself a 30 percent cut — caused a dustup when it became clear that one of Apple’s rules meant Amazon would no longer be able to link e-book buyers from inside the Kindle iOS app to the Kindle web store, where Apple wouldn’t get a cut.

But Amazon hasn’t updated the Kindle app since then, and as of this weekend the link to the Kindle web store remained in the app, suggesting a stand-off between the companies, or at least some awkward behind-the-scenes discussions.

Separately, as Amazon prepares to launch its “Appstore” — not “App Store,” mind you — for Google Android devices, the Seattle company has been making rumblings about expanding to other mobile platforms, giving rise to speculation that Amazon may be mulling an iOS app store, possibly resulting in even more competitive awkwardness.

Of course, Amazon also partners with Apple, not only by offering Kindle for iOS but also as a retailer of Apple’s products.

In that way, the whole thing is starting to feel a lot like Apple’s relationship with Microsoft, where each company knows it needs the other for specific parts of its business — but secretly wishes it didn’t.

Todd Bishop is co-founder of GeekWire.com, a new technology news site based in Seattle.

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