If you telephone a relative and ask her to give her son five pounds (or whatever) for his birthday from you and you'll give your daughter the same from her, that's hawala, or one of the other similar systems with different names.

If she says "actually, can you give both of your kids five pounds from me and we'll settle up next time I see you," that's also hawala, etc.

Assuming you live outside the USA, if you say to Bank A, that is your bank, "please transfer five pounds from my bank account to that of Mr X" that's banking.

If you say "please transfer five pounds from my account to the account of Mr X with Bank B," that's banking.

If you say to your bank "please transfer twenty US Dollars to the account of Mr X with Bank B," that's correspondent banking but you don't know it.

What happens is this.

Under US law, all US dollars that are not in cash are held in Manhattan. All transactions that are cleared between US banks are conducted in Manhattan. This means that if there is any illegality in any clearing transaction, it falls within the purview of the New York banking regulator and, also, the Manhattan office of the Department of Justice.

Because all non-cash US dollars are deemed to be held in Manhattan, if your bank wants to do business in US dollars, it has to have an account with a bank in the USA which, even if it is outside Manhattan, ultimately clears through Manhattan.

Even if Bank B is literally next door to Bank A in your own, non-USA country, the following is the process. In this example, Banks C and D are in the USA.

You ask Bank A to send USD to Mr X who banks at Bank B. Bank A sends a message to Bank C, its correspondent bank in the USA. It says "please transfer twenty USD to the account of Bank C, held with Bank D, for the credit of customer Mr X. Bank C sends the message. Bank D makes a book entry that it's paying to Bank B for the account of Mr X the amount of twenty USD. Bank D notes that, now it's handed over the money, Bank C owes it that amount when they next settle up. Mr X can now, subject to delays in the system, go to his bank and withdraw the twenty USD.

All correspondent banking works in the same way. The differentiating factor in the USA is that the USA claims global dominion over its currency wherever, whenever and howsoever it is used and that it claims the right to commence criminal action against anyone who uses US money to break US laws.

You will notice that, in principle, correspondent banking and banking as we usually know it is, in fact, merely a more formalised and better documented version of hawala or, even, the simple arrangements by which families simplify the giving of small presents.