The short answer is no, the iPhone is not an Android phone. While they are both smartphones--that is, phones that can run apps and connect to the Internet, as well as make calls--they are separate things and are not compatible with each other.
Think of iPhone and Android as being two separate brands, two similar but different tools to do similar things. A Ford and a Subaru are both cars, but they're not the same thing. A Mac and a PC are very, very similar, but they're not identical and, generally speaking, can't use each other's programs. The same is true of iPhone and Android.
There are three keys areas that differentiate the iPhone and Android phones.
1. Operating System
One of the most important things that sets these phones apart is the operating system that they run. The operating system, or OS, is the foundational software that makes the phone work. The iPhone runs the iOS, while Android phones run the Android OS. While all operating systems do basically the same things, they iPhone and Android OSes aren't the same and aren't compatible. The iOS only runs on Apple devices, while the Android OS runs on Android phones and tablets.
The other major differentiator between the two is what companies make them. The iPhone is only made by Apple, while Android phones are made by many different companies, including Motorola, HTC, Samsung, and Google. Any company that makes an agreement with Google, who created the Android OS, can make an Android phone, while no company but Apple makes the iPhone.
Both the iOS and Android run apps, but their apps are not compatible with each other. While the same app may be available for both kinds of phone, you'll need to get the app designed for your operating system in order for it to work. As of this writing (July 2011), there are more apps available for the iPhone than for Android.
So, while they're similar, the iPhone and Android aren't the same. When it comes time to buy a smartphone, you'll need to decide which one you prefer. To get started on that decision, check out this chart comparing the iPhone to some leading competitors.
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