Synthetic identity fraud is the creation of a person or business that does not exist, assembled from a combination of personal information, and then used to obtain credit, goods or services. The definition in general use across the payments industry reads: "Synthetic identity fraud (SIF) is the use of a combination of personally identifiable information (PII) to fabricate a person or entity in order to commit a dishonest act for personal or financial gain."
That definition is worth attributing carefully, because its status is unusual. It was developed by a focus group of twelve fraud experts convened by the Federal Reserve, working from fall 2020 to early 2021, specifically to fix a problem the industry had created for itself: multiple competing definitions meant the same losses were being classified in different ways by different institutions, so nobody could measure the scale of the problem. The published definition carries an explicit disclaimer that it is "not intended to result in any regulatory or reporting requirements, imply any liabilities for fraud loss, or confer any legal status, legal definitions, or legal rights or responsibilities", and that adoption is voluntary. It is a shared vocabulary, not a rule.
The distinction from ordinary identity theft is the one that governs everything else. In identity theft, a real person's identifying information is used as that person, so the fraud lands in that person's credit file and they eventually see it. In synthetic identity fraud the identifying elements are recombined into somebody new, and the new person is the customer of record. There is often no individual whose file visibly breaks, which removes the fastest detection mechanism the credit system has: a complaining consumer.