Secondary Surfactant
A cleanser is rarely one surfactant. There is a primary, doing the detergency, and then one or more secondary surfactants chosen for what they do to the system rather than to the dirt: build viscosity, turn foam into a finer lather, and soften the whole thing. Amphoterics such as cocamidopropyl betaine and the nonionic sugar-based surfactants are the usual picks.
The mildness is not a courtesy. It is an effect of mixing, and the standard explanation is that the two form mixed micelles which hold their molecules more tightly, leaving fewer free surfactant molecules available to interact with the proteins and lipids at the skin surface. A blend can therefore be gentler than either part alone at the same total level, which is why "contains a sulfate" answers less about a cleanser than people expect. The system decides, not the entry.
There is a labelling consequence. The second and third surfactants sit immediately below the first, so a cleanser's list usually opens with water and then a small cluster of them. Reading the cluster says more about how a product will feel than any single name in it.
Secondary does not mean inert. Amphoterics carry their own irritation and allergy profiles, and one of the most widely used of them is a recognised if uncommon contact allergen — which is why a gentle cleanser is still a product to patch test.