I was initially confused while trying to determine the name of this species, and apparently Linnaeus is to blame. My first inclination was to search online for wool and Dipsacus or teasel and discover what species were used for textiles. Some references pointed to Dipsacus fullonum, or fuller's teasel, as a likely candidate. This species was named by Linnaeus, and seemed to indicate that this was the species used by fullers (people who “bulked up” cloth woven by weavers, to make it feel more full). However, other references suggested Dipsacus sativus, or Indian teasel as the teasel of the textile industry, and ultimately this made far more sense to me.
What are the differences between the two species that bolsters that conclusion? Again, the Jepson Manual helps: Key to Dipsacus. Note that Dipsacus fullonum has more or less flexible receptacle bracts, ending in straight spines while Dipsacus sativus has stiff bracts with recurved spines. If you were going to use one or the other of these to bulk up wool, which would you choose? The one with the recurved spines to catch the wool and pull it. Confusion cleared up.
This photograph is from the small museum in the Mission Santa Barbara in California.
Photography resource link: for inspiration, the photography of Guy Edwardes.