They are maintaining the value of 1 USDT close to 1 USD at all times by minting more coins into circulation or burning some. Not sure about the tech details about how they do it, but if I wanted to create a stable coin that is pegged to USD I would (as a creator) call the smart contract to update the liquidity supply by calling an oracle that would tell me how many coins I should add or burn so the value remains at 1 usd. Now that oracle would take into account a lot of things to come to the conclusion of what to do with the supply to maintain 1 usd per coin (info from exchanges or coinmarketcap, how the dollar is doing, etc).
Hope that helps!
Yes, it's very similar. But in teter this is done in such a way that the whole is supervised by Tether corp, and I mean more so that I can free myself from any "distributor".