From a bank point of view there is no difference whatsoever!
A financial institution has a duty to ensure the origin of funds deposited with it.
I have a bank account and if I give someone my account number (IBAN etc) they can transfer funds to me. The bank doesn't know anything about the person sending the money (they are not a member of my bank)
Does a bank account with you function in exactly the same way as any normal bank account?
Can I link my paypal account to my bank account with you?
Can I set up a monthly direct debit to pay my bills?
Can my employer pay my wages directly into my account?
The bank knows what bank it came from and the account it came from. It is the other bank's responsibility to know their customers and the trail will be followed in an investigation.