This is a pretty basic question. I wasn't clear after a bit of research what types of Facebook apps one could create.
I think one kind is a web app which gets incorporated into Facebook web pages. I think it kind of works like an iFrame. Am I understanding this correctly?
I'm not clear about iOS and Android apps. Are they separate mobile apps that use Facebook authentication OR do they get incorporated into Facebook's own mobile app?
Canvas (resp. Facebook Web Games, as it is now known, after Facebook decided to name a new, more directly end-user facing feature "Canvas" for marketing reasons) and Page Tab apps are the ones where the content is shown on Facebook in an iframe. You can use the API & FB login on external websites, too.
Native Android and iOS apps are individual, stand-alone apps, they are not integrated into the official Facebook app; but are using the Facebook platform - login & API - to create a "social experience" for their users. Distribution of those apps to the end user usually works via the official Play/App store; in addition to the review Facebook requires, Google and Apple might require additional review before your app gets in there.