Android does have a visible file system but some Android install a file manager app like the Galaxy S, but most don't. You can however, find free file managers in the Android Market.
Files under those third party file managers, if you click on them, they would be opened by the app associated with them, like PDF with Adobe Reader.
Android Gingerbread now has a universal Download folder where you can see and open all the stuff that's been downloaded. Before that, downloaded files are accessed by one of the browser pages. In any case, Android has a transparent media scanner that scans on the storage and associates files with a parent app that can open them. That's why a music app will know where to find music files, and Adobe Reader knows where to find and open pdf files.
But there is another ability that you need to look for. Its called interprocess communication or IPC. That means an app has the ability to share information to another app.
iOS has this but its very limited. So far, Android is the clear champ when it comes to this.
If a browser for example, can share a web link to any app installed on the phone that is relevant for this, whether its GMail, Yahoo Mail, Facebook, MMS, Bluetooth, any Twitter app your installed, Delicious, Instapaper and on and on. Same with the Gallery app, where you can upload any picture to any service that's installed the phone (you don't really need an Instagram equivalent on Android). Apps install these services in a modular fashion to the OS; the OS has no need for updates to incorporate hard wired features like you would need on iOS and Windows Phone 7.
For example. Brand new, Android won't have the ability to share a picture from the Gallery to Twitter. Install Twitter for Android app, and the service is added to your Android handset or tablet.
That's why they say Android is open. And modular.
Another example. You cannot store web links from your browser or tweets from your Twitter app to Evernote for safekeeping. When Seesmic for iOS came out with this particular hard wired feature, they made a big thing out of it.
Yet, out of the box, every browser, every Twitter app in Android has the ability to send and save links and tweets to Evernote. just like that. The feature don't have to be built in on the app, its taken care by the OS through its IPC.
Android apps simply have a level of app intercommunication that I don't see on IOS. If an iOS news app has to send a link to Twitter, they have to post it directly, and the dev has to add this feature. In Android they don't have to. They merely utilize the universal share feature, and when you click on the Share button, you have a whole list of apps yo can send your link into. In our example, let's use Twitter for Android to post the link to Twitter.