That's where we part ways. Neither one of them are Bitcoin. Both are entirely IOUs. And yes, Lightning custodians happen to use Bitcoin as what they call those IOUs, but not even that is necessarily the case.
Strike, for instance, lets you send and receive zaps just like any other Lightning custodian, but you can choose whether your IOUs are denominated in Bitcoin or USD, or other fiat currencies based on your jurisdiction.
Same thing with Aqua wallet, which lets you receive either LBTC or Liquid Tether, both of which are just IOU tokens. Still custodial, too, just takes more people to collude to rug you, and they would have to rug everyone at once.
A Lightning custodian can denominate your IOUs in anything they want, just like eCash can. It's just that most of them opt to denominate your IOUs in Bitcoin rather than something else.
There is absolutely nothing intrinsically tying your balange in any custodial Lightning wallet to any specific or group of Lightning channels, or even to sats as a denomination of Bitcoin. Custodial Bitcoin of any type is equally just an IOU token, and is NOT Bitcoin.
