Typically the payment processors are not tasked to detect fraud. They get a single API call with a CC number and details and a billing address and they just check with the info the bank has on file. Most businesses do not decline the order even if the billing address is not a match; you have an option to ask your payment processor to decline the order based on AVS code (Address Verification).
To detect if an order is a fraud, more information must be fed into the analysis, and credit card details may not be needed at all. Usually, big rushed orders where the billing and shipping addresses are different and the order is put from an international IP may indicate a fraud. Also, if an order is put after a number of different credit cards were tried, possibly, it is a fraud. You can manually check these details for each order, if you get a handful of orders everyday. You can look at the google map for the shipping address and check the IP that the request came from. See how far they are from each other. Social engineering data is also a key; you can check poeple on LinkedIn to see if they exist and look legit.
But this can go out of hand, if you have a large number of orders. There are many fraud detection service providers that you can call their API, provide the transaction details, and they will give you a score indicating how risky the order is. Examples of them are SignifyD, MaxMind, SiftScience, Riskified, Kount.