For all practical purposes, ASA and ISO have become synonymous.
Prior to ISO, for many years in N. America we rated film using ASA... "American Standards Assoc."
Many other parts of the world used DIN... the "European" system or "Duetsches Institut fur Normang".
ASA is an arithmetic progression.... while DIN is logarithmic.
Much film, many light meters and some cameras showed both scales throughout most of the 1960s through mid-1980s.
ISO or "International Standards Organization" was first discussed in 1974, published in 1979 and began being adopted in 1984. Initially it was a combination of ASA and DIN. For example, ASA 400/DIN 27 rated film was instead shown as ISO 400/27.
But over time the DIN portion of that number has been dropped so we now only see the ASA equivalent being stated almost universally. There's almost no reference to DIN any more. ISO 400 is the same as ASA 400.
Historically, ASA was introduced in 1943 and DIN in 1934. Prior to the late 1950s when those two became the most widely used standards, there were a number of other systems in use. Weston and General Electric each manufactured light meters and had their own, similar scales. Those two had a lot of influence on ASA. BSI or "British Standards Institute" is another sensitivity scale, pretty closely related to DIN. The Soviet Union had their own GOST, which was similar to ASA. The earliest was Warnerke, named for the inventor of the first sensitometer around 1880, which used a standard of measurement developed along with the device. There were a couple other now-archaic sensitivity measurement scales in use prior to WWII.
Much more info here:
https://en.wikipedia.org/wiki/Film_speedThe consolidation and standardization of sensitivity ratings have been driven by two major factors. As film and other photographic products were being improved to offer greater sensitivity to light, new measuring methods and scales were necessary. In addition, increasing globalization of products, especially after WWII, also served to narrow the field.
Makes me wonder if we'll see something new in the future, now that some digital cameras have sensors with ISO sensitivity in the hundreds of thousands or even over one million! The numbers are getting so big and cumbersome that someone has probably already proposed changes to the way we talk about light sensitivity. Or maybe we'll just use Auto ISO all the time and not worry about it!