DAI is not algorithmic at all, but it is controlled by smart contracts. For $1.00 of DAI to be minted, a user has to post somewhere between $1.25-$1.50 of collateral. The act of creating DAI is literally that of taking out a loan. Over time, your debt to the system accrues interest. If your collateral falls under a certain price threshold, the issuer of DAI (MakerDAO), will seize your collateral to close your position. You keep the DAI, and MakerDAO liquidating you keeps the system above water and DAI at the dollar peg.
Algostables are not collateralized at all. They're more akin to ancient gold coins. Think of Luna as a small piece of gold. When UST is created, the Luna is "melted" to form the UST. At any point, the UST can then be "melted down" to get the Luna back out of it. From a certain point of view, UST literally is Luna.
algostable != overcollateralized stable. Being an overcollateralized stable means it's actually backed by something, even if it's USDC. An algostable is backed by the sister token (eg: LUNA), and relies on faith and confidence in the sister token.