I guess you meant "cold" wallet sitting on air-gapped device that was never been online and in the future will never go online.
There is no difference between an offline- and a cold wallet.
"Offline" does not only refer to the internet, but to any communication interface (wifi, bluetooth, ..).
Therefore each cold wallet is indeed an offline wallet and each offline wallet is a cold wallet.
I see this things differently. You and me have already discussed all relevant stuff and I think there is no use to start our dispute again here. You stayed with own opinion but me with mine. For who's interested, I'm giving the link to our discussion that has started since that post