For years keepers of animals have been paying out the wazoo for products dedicated for cats and dogs, when we could buy the exact same formulation much cheaper if we would have purchased the identical product marketed for cattle, horses and pigs
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I'm a restricted use pesticide applicator. I know the importance of following instructions. However, the government regulations are sooo strict on making the companies list all chemicals in the labeling. If there is a difference in formulation, it will be right in front of your eyes.
If you feel safer with the one marked for chickens, by all means you may go ahead and pay triple or more for an identical product.
In the case of pyrethrins, nowhere does any vet differentiate between brands or types. They even recommend putting a diluted mixture directly on birds for some infestations. Farmers, ranchers and hobbyist have for many years saved untold thousands by reading labels and saving a lot of money.
Having said all this. If it had a warning NOT TO USE on chickens or around chicken housing and chicken feed, I would heed these warnings.