When using terminology like "Air Gapped" what is your first impression of it?
When I see someone say they have an air gapped network, I think it to mean that the network is separate from the rest of the organization (through a physical disconnect), and that Air Gapped, does not imply the lack of internet.
Air Gapped != Without Internet
What's your opinion?
An air gapped network is indeed physically isolated from other networks, but the key yiur missing is that it is also isolated from the Internet. The primary characteristic being lack of any connection to outside networks, including the internet.
It's not the "connection to the outside" that violates the air gap, the issue is that if BOTH networks connect to the Internet or any shared network, it clearly isn't air gapped. Air gapped systems can never talk to each other without a different mechanism passing messages in between that crosses the air gap.
You misinterpreted what I wrote. Coupled with the first sentence, it's clear. Also, outside being outside said network, not necessarily public networks.