What defines a Hardware Wallet?

So I’ve read the Parity Signer Mobile App wiki, but I’m still confused about what it does…

It would seem that if you dedicate a mobile device to this app and remove all the connectivity, then the Parity Signer software would meet the interface and storage requirements to be considered a wallet. The air-gapped + strong encryption bumps that up to hardware wallet by my definition.

However, if you don’t dedicate the phone to this purpose and are simply running the app on a normal smartphone, I wouldn’t consider it more than just a mobile wallet. The overhead to actually set this up properly seems very high, including both steep hardware requirements and usage requirements. Too many ways to mess up, so IMO it’s not a great solution in terms of high security for the average user. Certainly no worse than any other online wallet though.

I can loose a hardware wallet like my TEZOR - but when loosing a “offline signer” like the parity signer - this is a problem …

Why is losing the offline signer more of a problem than losing a TREZOR/Ledger? You are instructed to write down your recovery phrase when setting up an account - is that not something that can be used to retrieve private keys? Or are you saying that somebody could compromise the Parity Signer much easier than the TREZOR?