I'm not clued up on money laundering tbh. I know it's to 'clean' money, but I'm not sure how entirely. To assume either of your scenarios; someone sends me extra money in 'error' and I then refund them the overpayment - in what way am I out of pocket or in danger of having money taken from my account without permission?
There's a common scam where they'll pay too much (or you may be approached to cash a cheque, transfer £X to somewhere else and keep the rest as a service charge) by cheque from a foreign account. You'll see the cheque clear, and then refund the over payment, and assume everything is good. The problem is how fast foreign banks will process cheques.
Let's say that it clears after the 5th working day. Normally the money goes into your account, and you think that's the end of it. What has actually happened is the cheque has passed provisional clearance, and that there's nothing considered untoward. A short while later you then get a message from the bank letting you know that the cheque is fraudulent/been cancelled/whatever, and they're taking the money back from your account. The fact that you've acted in good faith doesn't matter, and even if it means you going into an overdraft, the bank are (rightly and legally ) taking their money back.
What's happened in the period where everything was fine is the foreign bank's systems have finally caught up, spotted that the cheque is janky and told the UK bank that they won't be paying out.
The banks used by scammers are usually small banks that aren't part of any central network or owned by bigger banks. They'll usually have the slowest systems (I've heard reports of it being over a month later until it's been spotted), so the chances of catching the scammers are small because they use this time to distance themselves. These scammers will usually work in "shifts" where they'll make the same offer to many others, and then as soon as the clock starts ticking for people to start realising, they disappear, phones go dead, e-mails not answered, sometimes change location, and then rinse and repeat with new details.
Before Europe starting getting it's act together regarding money laundering, a common way of doing it abroad was setting up as a money exchange. You'd see exchanges offering crazy amounts to the pound (usually around 10% more). and you'd wonder how they were doing it. What was happening was the dirty money was heading out the country, and was used to buy foreign currency. At this point the exchange gets set up, and they start selling at the crazy rate, and then if the authorities started getting nosey, they'd simply close and reopen elsewhere. So how did this make money?
When you're laundering money, it's rare that you'll ever get a 100% conversion rate, or at least legally and correctly without people asking questions. You can expect to take a hit of around 30-40%, and it's viewed as a business expense. The crazy exchange rate will be part of the cost, but it's also advantageous as it allows them to launder a large amount of cash because of the amount of business they're doing (every tourist is using it). The people running the exchange also take a cut, and when the money is handed back to the criminal (minus costs) it's given the illusion of being clean.
There was a good scam when we were part of the EU and the pound was strong against the Euro, which offered a very good conversion rate, but was pretty unwieldy. You'd be offered a week or two in Spain for free. All you had to do was fill up a case with baccy and cigarettes, also paid for, and bring it back the UK. The baccy and cigarettes would be sold for the equivalent Euro price in pounds (€5,00 a packet would be £5.00). The pound was strong enough at that point, and a cheap holiday would pretty much be paid for with the £/€ exchange rates. The main problem was the authorities taking an interest in flight lists. You could pretty much guarantee someone doing it once or twice would get through, but someone doing it once a month would get pulled. Even if the person managed to get through with the baccy (it's rare with a case full but it does happen) then that person was useless after that. Either way, at that point you've got cash that is laundered and relatively clean. It was just a pain because you needed people to take the holidays and the hassle of shifting the product.