Read carefully what this wallet says - "create from an Offline/Watching-Only wallet to be signed by the computer with full wallet".
So ?
How is that related to the fact that each cold wallet is an offline wallet and each offline wallet is a cold wallet ?
Deciphering for you - Offline/Watching-Only wallet is a hot wallet running in offline mode on online computer that is capable to create the raw transaction to be signed by full wallet running on air-gapped computer.
"hot wallet running in offline mode on online computer"
This doesn't even make sense.
You can
not run a hot wallet in "offline mode" on an online computer.
There are 2 options:
1) It is a hot wallet. Then an "offline mode" itself does not exist. Even if your PC is offline for a specific timeframe, it still has nothing to do with an offline wallet or so-called "offline mode".
It it is stored on an network-connected device, it is a hot wallet.
2) It is an offline wallet which means it is stored on a device which will never be connected to a network. In this case it has nothing to do with a hot wallet.
The full wallet running on air-gapped computer = cold wallet. Period. Bold.
Yes. And another term would be: offline wallet.
If your private keys are not on an always-offline and air-gapped device, this is not an offline wallet and not a cold wallet.
I agree with you that armory did phrase that quite ambiguous.
However, by pure logic..
Either your private keys are stored on a device which is connected to the internet / a network (even if only for a short amount of time): Not am offline wallet, not a cold wallet.
Or, your private keys are stored on an offline device / not connected to any network: Offline / cold wallet.
There is nothing in between.