The swap occurs directly over lightning. Both respective fiatcoins have to have liquidity (but the sender and receiver are basically the liquidity in this case) and to the lightning network, and even to each user, which currency at the beginning or the end is irrelevant. The payment is being settled in sats and converted on both ends.
It’s less taproot assets specifically, and that you can send these assets over the Lightning network for settlement.
Right now if you have tether and want to pay me, I HAVE to accept tether, or you have to go to an exchange, make an account, and swap it to USDC, and you hen download and install a USDC wallet to send that to me instead if I want to receive it. Which nobody is gonna deal with, they will simply use Tether/USDT for the sake of simplicity. So there’s huge lock in, similar to “CashApp users can only send money to CashApp users.”
However, as taproot assets, the swap to sats in a Lightning invoice is built in. So as long as the sender and receiver agree on the value (which is just the invoice amount), I can “zap you” USDT and I don’t even have to know or care what you receive it as. You could just be taking the sats, USDC, ruble coin, yuan tokens, some bitcoin based shitcoin, who cares? That’s simply your choice and the thing actually transmitting the value, is BTC. It becomes this bridge, and ironically kinda becomes this “any currency to any currency DeFi system” without needing a coordinator, or stupid blockchain, or order book, or ETH VM, or any of that garbage. It just needs a sender and receiver and simple agreement on the value to exchange. It’s the nodes at the edge run by tether or some bank or Coinbase or whatever that need to build liquidity to accept their token and forward sats that creates a foundation for this, and after that bootstrap, the barriers just kinda fall away and there’s less reason to use any specific stablecoin/fiatcoin instead of any other simply due to how much it’s used, but instead you would use specifically what you *trusted.*