Remember the original iPhone launch? The outrage that it wasn't possible to create 3rd party apps for it? Why was it such a big deal? Especially considering that Apple just had released their first phone, with some music playing capabilities...
Or did Apple actually release a phone?
When looking at the big picture, I think what Apple did... was a general purpose device, with touchscreen optimized user interface. Yes, it happens to be able to make phone calls, but it can also do many other things.
The reason people carry a mobile phone around, is the ability to be connected to other people and other people being able to connect to you, when needed. Since people are not so comfortable with carrying big bunch of devices (requires more space, weight, ...), they quite often like the fact that they can use the phone also for other purposes than making calls.
Many owners actually use their iPhones for many things that are not about calling or texting, hence the wild popularity and download rates for thousands of apps in the App Store. Personally I'd probably be quite comfortable with an iPod Touch (a non-phone), if it weren't for the fact that internet has to be accessible from everywhere (cellular data), and that it's nice that people are able to connect to me via conventional ways, even if it's not that often.
Since iPod Touch carries the stamp of "iPhone without the phone", are the users of the iPhone and the iPod Touch using their devices for mostly the same purposes (except calling)? Probably not. Games have been hugely popular in App Store, and I'd be willing to bet that pretty many of those games are being played on iPod Touches..., because that's what the "younger kids" are having. It's a secondary device, mostly a portable game console, which they can carry around. No need for expensive phone plans, just keep the cheap phone, with maybe pre-paid contract. As a bonus, in home, school and other networked places, it becomes nice portable web and social device.
It's just a hunch, but women seem very interested in small portable music players to carry around. All those almost jewelry -like iPod Nano's and iPod Shuffles. It's humming along in gym, as well as on the way to work and back. For that, iPod Touch is a bit too big... unless it can provide enough appeal beyond having nice metal mirror on the backside. For some it may have that desirability, but then the lack of ubiquitous connectivity (for all the social apps) points towards an iPhone...
iPod Touches and iPhones are being used in homes, but there they need to compete with full-blown personal computers, as well as with wall mounted big TVs. And there, the small screen, no matter how high the resolution is, starts to lose it's shine. And currently the apps enabling Create and Modify activities are only starting to appear in the App Store.
For casual organizing of life, like noting down upcoming events, making shopping lists, sending reminders to friends... The small, instant-on touchscreen devices still can easily overtake TV or computers. But for big time entertainment, or for "getting things done", it falls a bit short.
...
In some ways, iPad is more of the same. It's still the same idea as iPhone already was, a very general purpose device. So it's not so much of a question what all kinds of things are possible (pretty much anything), but who is using it, in what context.
The only major difference to iPhones and iPod touches is the physical size of the display, which then ends up affecting the size of the device, the weight and consequently the ways to hold it and the portability of it.
Being more luggable and instant-on than a laptop, some internet-oriented road-warriors have found iPad being able to replace, at least partially, the use cases for laptop. It is more relaxed, almost leisurely device to use, compared to a full-blown laptop. And showcasing things to a client, on-the-go, is quite likely more attractive and immersive on a iPad, compared to a laptop screen (just give the iPad to the clients waiting hands). All in all, it will still take quite some time before iPad is a valid competitor to laptop for road-warriors though.
Compared to the iPhones and even iPod Touches, I think the iPad will spend much less time on the move. For an average person, it's probably a "device at home", "device at work" (e.g. medical field), or some other static context like that, with only occasionally taking it along, for example to show latest family photos and -videos to grandparents.
As a "home device" it probably is more entertainment oriented, whether it's news, books, web, social or games. It's the device when you want to "quiet down" on your own, to do your own stuff, rather than sit, agree on and watch the same TV programming with rest of the household. So you might sit on a sofa, or lie down on bed while toying with iPad.
Two groups of people who will actively use iPads are kids (especially younger than teens) and the elderly. The extent of it might still surprise some, in a year or two from now, as those groups are not traditionally typical for using the latest tech.
For kids the almost irresistible draw on iPad is it's intuitiveness. Just Google for iPhones and 1-2 year olds and you will get the idea. There are already, and there will be even more iPad apps specifically for kids. Parents have the power to choose what apps get on the device (by buying them) and kids have the freedom to explore the iPad without the need of parent to watch or guide over the shoulder. It's a win-win situation. Plus there's no need for separate game console, or DVD player. Some of the best selling children's books become animated and interactive, becoming even more attractive, and self-learnable.
Maybe un-surprisingly, the elders get attracted to iPad for the same reason the kids are. It's their "first computer" that they can actually use, without being intimidated or having fear of getting lost. There's the trusty, single, big, physical, black "panic button" that always gets you to where you started from.
And this is just the beginning of the journey.
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Update: Mr. Bray points to tablet's advantage for (physical) shareability. Good point.
