Where did Asperger's (and PDD-NOS) go?
The terms Asperger's Syndrome/Disorder and Pervasive Developmental Delay-Not Otherwise Specified (PDD-NOS for short) have been dropped from the mainstream diagnostic system used by most mental health professionals in the US. The "big book" cataloguing mental health conditions in the US is the Diagnostic and Statistical Manual of Mental Disorders published by the American Psychiatric Association. It is commonly referred to as the DSM for short, often with a version number. The current version is the DSM-5.
While the DSM-5 was published in 2013, it has taken a number of years for the revisions to be adopted by mental health professionals. This is especially true for autism and related disorders where people are usually diagnosed once at a relatively young age.
The DSM-5 made some major revisions to how autism and related conditions are described compared to version 4 (usually written as DSM-IV or DSM-IV TR). Under DSM-IV there were three categories for people with autism: Autism, Asperger's Disorder, and PDD-NOS. Over time it became obvious that differences between the three categories weren't very helpful and probably represented subtle shifts in severity and language abilities.
In the DSM-5, these three slightly different presentations were collapsed into a single broader category: Autism Spectrum Disorder or ASD for short. Materials published at the time of the DSM-5 release emphasized that people diagnosed with any of the three categories in DSM-IV should continue to be provided with an ASD diagnosis unless there were concerns for a misdiagnosis and a new, full evaluation shows they do not meet criteria.
One thing the DSM-5 did not change is the labels that people in the autism community adopted to identify themselves. There are many people diagnosed with Asperger's Disorder in the prior system who prefer that term to describe themselves and have built communities around the term to identify themselves.
For nondiagnostic use, Asperger's Syndrome and autism are both terms people use. Sometimes Asperger's is shortened to Aspie. These terms are still generally used in books and other publications.
If a formal diagnosis has to be provided to access services, then the diagnosing professional will likely update the description to match ASD in the current system. This isn't really any change from a prior diagnosis, just updating to match current terminology. Insurance companies and health systems are often sticklers for these details. Claims and payment can be refused if current terms aren't used.
If questions come up about former diagnostic descriptions versus current ones, it is always a good idea to ask questions to the person making the changes.