The answer is conditioners. Milady names it directly, alongside shampoos: shampoos and conditioners are examples of emulsions used in barbering services.
The book also notes a practical shelf-life rule tied to this classification: cosmetic emulsions should be used within one year of purchase, since emulsions can separate or degrade over time. Soaps, powders, and hair tonics are all real barbering products, just not the ones the book specifically classifies as emulsions.
Milady Standard Barbering, 6th ed., Ch. 7 (Basics of Chemistry), p. 186: "Shampoos and conditioners are examples of emulsions used in barbering services."
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