I haven’t seen the original form of linoleum made it installed anywhere on any jobsite I’ve ever worked.
I realize the term has been co-opted by the plastics industry, but if you’re specifying the original linseed oil recipe from the 1870s, you need to specify that.
Vinyl and linoleum have been interchangeable terms in modern parlance for several lifetimes at this point.
I’ve heard & seen vinyl and linoleum used interchangeably over a lifetime, and I don’t believe the original recipe is still manufactured so far as I have seen.
Even if it is still being manufactured, the vast majority of people talking about linoleum seem to mean vinyl. I’m going with the average vernacular, and still stand by all my original points re: vinyl.