What do we call it, then? Because the terms you've been using aren't correct. It isn't like ETH where I swap it via an exchange for Bitcoin. It isn't like a stable-coin like Tether, or even side-chains like Liquid.
When I have 100 Satoshis in my Lightning wallet, it is because there is a channel based on a wallet with those 100 Satoshis in it.
In some sense, I suppose the IOU language kind of applies, compared to self-custody Bitcoin in my own wallet. But, then again, if it is under my control, not really either. Those 100 Sats in my Lightning wallet can be swapped, by me, at any-time into my on-chain wallet.
It is more like if I'm taking a loan from myself (if self-custody). Yes, if you are using a custodial Lightning wallet, those Satoshis are under control by someone else (but same technology either way... they are just as real, just not controlled by you, ultimately).
