A bit off topic as it is not US based, but one of my on-line banks ( as I signed up, transferred funds, etc..... exclusively on internet ) allows me free international transfers. On my smartphone, no human intervention.
P.S. I am a bit confused by the difference between a wire and a transfer, so excuse the post of it is not revelant.
Its the same thing basically.
The term wire (AFAIK, its just a term and not a definition of a process) is most widely used for international transfers of monies. It does cost money, a fee of usually $45.00 USD
The term transfer, accomplished the same, but its most used for local movement of monies within a country. Here in the DR, the cost is cheap
Then there is the ACH which is nothing but another transfer of money but this one is completed by the Automated Clearing House through a network of banks. It has no cost at least in the USA
The key to them all is the time it takes for the money to be cleared.
A Wire clears instantly, so does inter-banks transfers, ACHs usually take up to 3 days.