multi
I understand the networks are different but I still don't get it how those online exchange services do it that can't be done locally.
Exchange service has multiple wallets with coins in each wallet. You send them one kind of coin, they send you some of their other kind of coin. They don't "exchange between the two".
So for example, they service is running BOTH a Bitcoin wallet AND an Ethereum wallet. When you send them some Bitcoins to exchange for Ethereum, they notice the incoming bitcoin transaction. They do the math to figure out how many Ethereum that should be. Then they send you the calculated amount of
their Ethereum from their Etherium wallet.
Later someone else sends the service some Etherium to the service's Etherium wallet. This other person wants some Bitcoins. The service notices the incoming Etherium transaction. They do the math to figure out how many Bitcoins that should be. Then they send that person the calculated amount of
the Bitcoins from their Bitcoin wallet. Most likely the some of the bitcoins that they are sending out are bitcoins that they recently received from you.