SWIFT US$ transfers clear through its New York partner bank, which means that when you send money from your bank, the clearance will hop through some intermediary banks to New York, where the Recipient Bank (eg., Chunghwa Postal Bank) has an account, and then your Recipient Bank will push the money to your Recipient’s account.
If your bank doesn’t have an account in the SWIFT partner bank in New York, then it has an account in a bigger bank that does. At the SWIFT partner bank in New York, the instructions that began in your local bank are used to transfer US dollars to the Recipient bank’s account in the SWIFT New York partner bank
This all typically takes 3 to 5 days - someone posted 4 to 7 days and that’s a fair estimate, too
Here is how SWIFT works, it’s history, and recent troubles…
When you use Bank Transfer to send via TransferWise, that website acts as a facilitator, enabling LOCAL transfers that do not have to clear through New York. This is why it is faster and cheaper. You just have to trust TransferWise – and most of us do. Very much (it’s awesome!)
This explainer video does a good job - jump to the 5 min mark to get to the part about using your bank to send thru TransferWise
I do NOT yet know how to send via TransferWise to Taiwan (except via their Debit Card, which you need to request separately after you set up a TransferWise account). I’ve been having money sent to my HSBC account in HK and then I send it for free to my HSBC Taiwan account using their internal “global banking” transfer system