Welcome to nostr, and so that your first response is worthwhile, let me disagree with you!
In lightning, if you run your node software correctly, nobody can steal from you.
This means an offchain utxo settled in a lightning channel is "as good as" the utxo onchain, and thus both fall under the base money category.
However everything else, like account based (wallet of satoshi), ecash based (cashu, fedimint), sidechain based (liquid) has a third party (federated) custody model where you are at the full mercy of the custodian, this makes it fiduciary media, money warehouse banks with notes that are redeemable at par for base money (onchain or lightning).