That's oversimplified of course. The iPhone OS is a recompiled version of OS X based on the same Darwin foundations as OS X, missing many of the components required for a desktop OS, but modified with a lot of components that are necessary for a touch based mobile device.
I wouldn't think that Apple would take the version of OS X running on the iPhone and modify it to run on a tablet. I think it's far more likely that it would take whatever version Apple is using for development of OS X and migrate that to a tablet in the same way it did with the iPhone. They would share the same lineage and perhaps a few of the components, such as Cocoa Touch. And they would all be a subspecies of OS X.
Despite these shared underpinnings, it's pretty clear from Microsoft's failed experience with the tablet form factor that desktop apps simply don't translate to a useful experience on a tablet. These apps, like iTunes and Excel, require or expect precision interaction via a mouse and text entry via a keyboard. That simply doesn't work on tablet. So yes, entirely new apps will be necessary to take advantage of the benefits of this form factor.
What seems to be confusing to a lot of users here is the distinction between the desktop UI, which uses Finder, and the iPhone's UI.
Are people saying that Apple should discard Cocoa Touch in favor of some other development tool for this yet to be released device? I would say that would be a huge mistake. They should leverage and expand Cocoa Touch to facilitate migration of apps to a new device.
Or are users here saying they don't like the way the iPhone arranges apps on the screen and thinks that Apple will use the identical interface on a tablet? I see it as unlikely that Apple will use the identical interface, but I do think that there will be similarities reflecting their shared purposes and utility. Regardless, the iPhone's current UI is far better suited for a tablet then OS X Finder's is. The hierarchical file structure of a desktop OS is simply too cumbersome for a mobile device.
Regardless of this, I would bet, and in fact support, and app store for a tablet. Forget the benefits this has for Apple's bottom line. The advantages for the users are apps that work. Sure, there is a price to pay but those unsupported app have found their way into the Jailbreak community. Having used Windows Mobile prior to the iPhone and as far back as when it was a PDA only option I definitely prefer the ease and security of the app store. And if users really want that mythical robust marketplace of quality apps they really should go to the competition. Is Apple doing a perfect job with the app store? Of course not and I wouldn't argue that they are. They are, however, improving, and it is hugely preferable to the alternative of unstable, buggy, and insecure apps found on other platforms.