The very best foaming products contain at least two surfactants.

The classic foaming surfactants are anionic such as sodium dodecyl sulfate (SDS) and sodium laureth sulfate (SLES). They form great foam heights but the bubbles collapse really quickly.

Foam stabilizer chemicals are added to consumer products, such as laureth-3 or 4, cocamide DEA. These usually don't make foam by themselves, but what they do is like iron rebar in concrete, they reinforce the bubble that has formed.

Baby shampoo is a nice example. It's usually the mixture of SLES and cocamido propyl betaine (an amphoteric surfactant). The previous stabilizer mentioned is fantastic, but it is a skin irritant and burns your eyes. The amphoteric cocamido is very mild but less effective, hence, you need a lot more of it (higher cost) or you get a lower foam height / short stability time.

The difference between two-product formulas and solid bar soap, is the bar soap is usually a single surfactant maybe with some glycerol added. The bar soap needs a shitload of mixing energy to make a stable foam. You need to use a foaming brush and lots of stirring to input enough energy so that the molecules align correctly and get the best ratio of air/water/surfactant. Even after all that energy is put in, it still doesn't last as long as a two-surfactant mixture.