Correct, neither Wise nor Swift are banks.
Swift is simply a transfer protocol. Wise will let you hold money on account, but because it is not a bank that is not recommended for larger sums or a long amount of time.
If Wise has any reason to question the validity or legality of your account you could find your funds frozen.
You can use either Swift or Wise to transfer your funds to a new account safely, though with much larger transfers, I would suggest you approach Wise customer service to confirm the transfer is copasetic before you pull the trigger.
Also depending on the size of the transfer, Swift may be the better policy due to its fixed rate nature. Wise is very reasonable for smaller regular transfers, but could get expensive if sending a few hundred K.