The names on a cordyceps label do not map onto one organism
Paecilomyces hepiali, one of the commonest label names, is a fungus isolated from wild Chinese cordyceps rather than that organism itself.
What the study found
No agreed classification exists for the fungi sold as cordyceps
Paecilomyces hepiali, one of the commonest names on a retail label, is a fungus isolated from wild Chinese cordyceps, not that organism itself. The wild caterpillar fungus, Ophiocordyceps sinensis, goes by a different name again in its asexual form: Hirsutella sinensis.
The caveat · China's industry, not Western shops
This is a review of the Chinese industry rather than Western retail, and it describes those names rather than counting how often they appear. One author works for a cordyceps manufacturer, though the paper argues against loose labelling rather than for it. The authors say two of the fungi they discuss need further study before their place is settled.