It depends on how each developer has implemented it. Sorry, but yes that means nothing definite can be said about it.
Yes, for most apps the obvious choice is to personalise it to the user account
(for instance, Contacts and the other standard Android PIM apps work this way). This, IMHO, is the Right Way to do it for user-centric software (such as the standard Android PIM apps, games, or note-taking apps). This would mean that I could use my software on all
my devices (not necessarily simultaneously, but also if I were to buy and switch to a newer device) -- but only in so far as my devices "act as one" in the sense that they all sync to the same mailbox, address book, and so on. That is to say, if I wanted to share an app --but obviously not my Google account-- with my wife, I'd have to invest in two copies of the software. To me this seems very reasonable.
Some apps are personalised to one specific device
, so you'd have to register twice if you wanted to use it for two devices. This, IMHO, is well suited for specifically device-centric applications (for example Wave Secure), but should definitely not be used for something user-centric (a game or note-taking app) because this model would not play well if a user were to buy and switch to a newer device ... it smacks of Microsoft-style licensing.
I think it's a Very Good Thing that the Android OS does not support DRM; but unfortunately, it also means that application licensing and protection is not well supported, forcing developers to roll their own protection and/or enforcement mechanism.