A bit more generic than that; there's no global setting where user says "this is my preferred App.Net app". When user hits Share in any app (many apps provide such a feature), a menu appears with all available apps user might want to share to. Any app can opt in to be in the menu, based on MIME type of what's being shared.
Does it take you out of the app or bring up a part of the other app which you use to share and then dismiss and you are back exactly where you were before you attempted to share?
That's how it usually works though there's a lot of flexibility. In some cases, it might not even be interactive at all, e.g. adding to your Pocket queue, you'd just hit the Pocket menu item and you're back where you were.
Apps can register to handle URIs, which can be local, or something like http://*.reddit.com/* so whenever a link to reddit is found in say an email or web page, you can choose how to handle it, either via the browser app, or a reddit client.
