I want a secure wallet that is strictly offline, untouchable.
Can someone tell me what the difference between these two are?
In a general sense, they are referring to something very similar: part of a cold-storage scheme.
WIthin Armory, "watch-only" means you're simply watching a wallet, probably not owned by you.
"Offline" means you're watching a wallet that is owned by you, but the keys are on an offline computer, and you're simply watching it from this online computer.
When you import a watching-only wallet, it is by default not marked as your own (and thus labeled "Watch-Only"). You have to explicitly tell Armory it is your wallet in the wallet properties under "Belongs to:". Then it will switch to "Offline" and its balance will be added to your global balance. But changing that value doesn't really change anything: it's still a wallet that only has public keys, and you can't use it to spend money, only see transaction history and receive payments.
