I've been a graphic designer, active in the industry since 1982 ~ I can email files to a printer in Michigan and one in Minnesota, and print a job locally, and they theoretically should all match... IF the printer follows the PMS system. Each color is assigned a number... so If I design a logo with hot pink & deep purple, I can give those PMS numbers to any printer, and if they are reputable, will hit the mark right on.
It would be wonderful if the fabric industry would match, would make my life easier... but dye lots make that impossible. Even tho good mfg's try and be very very precise with their fabric print runs, there are still variances, even with the biggies list Waverly and Hoffman and Moda. Look at a bolt you just got, and one from 1 year ago. You'll see slight color diffs!
Another thing is, if you have an "old" PMS book, the colors could have faded if the book was not stored properly... I was told in college that my PMS book should be replaced each year. Couldn't always afford that, but I took very detailed notes on client jobs, so I always had PMS numbers logged.