A "surfactant" is nothing else than a classier, easier-to-sell term for soaps, detergents, and foaming agents.
Without getting too much into chemistry here, we can classify "mild surfactants" in 3 categories: anionic, cationic, and nonionic.
The first type, anionic, are surfactants that are cheap to produce and thus more popular among shampoo manufacturers. This could include alkylbenzene sulfonates, soaps, lauryl sulfate, ethoxylated propylene glycol, di-alkyl sulfosuccinate, and lignosulfonates, among others.
The second type is the most expensive of the three and mostly used as corrosion inhibitors within industrial settings.
Now the third type, nonionic, is the holy grail of surfactants and the one you need to look for when selecting a shampoo for your pet. It provides the same foaming effects we all humans cherish in a shampoo without the chemical harshness of their cousins.
The most common in this category is Decyl Glucoside which is 100% derived from vegetable origin (coconut) and biodegradable. Because of this natural base, this true mild-surfactant helps maintain skin balance without risk of dryness.
It is imperative for you to research and find out the type added to your pet's shampoo whenever you see "mild surfactants" listed as an ingredient. A manufacturer proud to use only the best ingredients will either include "plant-based ingredients only" or a high organic percentage somewhere on the label. If you don't, chances are you are dealing with the cheap kind of surfactant and you should never use it on your pet.