Also, technically the value of UST was fully backed by LUNA, until the total market cap of LUNA dipped below the market cap of UST, and then it wasn't.
IMO it's not the collateralization that makes something an algorithmic stablecoin, it's the currency is managed entirely by on-chain smart contracts, as opposed to Tether or USDC etc, which are managed manually by humans working in a room somewhere. Who knows though, I just made that definition up. The algorithm that manages DAI is pretty rad, so it seems unfair to deny them the status of "algorithmic", but that's fine.