I've been trying to understand the differences between the AISI and SAE naming systems, but haven't been able to completely figure it out yet. It seems like sometimes they are considered the same, but sometimes they are not? They both have 4 digit codes and seem to overlap fairly well based on my reading of this article .
Here is a brief mention of the history of the coding system, which may clear the confusion.
"The early 1940’s witnessed the development of a coding system for the classification of different types of steels. Designers, heat treaters, draftsmen, and engineers were able to obtain specific information on the types of steel along with its grades. The coding system is known for its efficient classification of steels as it uses the standards from the American Iron and Steel Institute (A.I.S.I.) and the Society of Automotive Engineers (S.A.E.)."
"For many years, certain grades of carbon and alloy steels have been designated by a four-digit AISI/SAE numerical index system that identified the grades according to standard chemical compositions. Since the American Iron and Steel Institute (AISI) ceased writing material specifications (in 2017?), the relationship between AISI and grade designations has been discontinued. From point of edition of the 1995 Iron and Steel Society (ISS) Strip Steel Manual, the four-digit designations are referred to solely as SAE Designations."
So, in general, the standards are the same when the 4 (or 5) digit designations are identical (AISI 1015 = SAE 1015), but it is prudent to check both.