Some sodas have ingredients that change surface tension (edit: surfactants and other chemical additives) One is actually lactose, the sugar in milk. I used it when I made my own root beer and it creates a really thick foamy head and a slightly creamy texture.
These tend to be the darker sodas as the color of surfactants is hidden by the food coloring. Plus a clear soda is supposed to feel less thick and syrupy as it kind of looks like water so in our minds we want it to feel closer to water than syrup.
Sodas contain fizzy water, sweetener, and an acid (among other stuff). The first two sodas you mention are flavored with phosphoric acid, and the second two are flavored with citric acid. I don’t know for sure if this is the active difference, but if you look at the ingredients lists of coke vs. sprite, it’s the main thing that differs between them.
Foam is a combination of protein and polysaccharides (e.g. starch). This is why many beers have thick persistent heads of foam.
Root beer makers add things to help increase the foam. The root extracts in traditional root beer likely added some of these things. Colas contain cola/kola nut extracts.
For home soda makers you can buy products like this: https://www.sodacentre.com/products/beer-heading-powder-25g
Many sodas are just flavor, acid, and sugar/sweetener. So nothing to keep a head of foam stabilized.
You’ve never had a mtn dew or sprite explode (fizz over) on you after shaking it?
Others in the comments are mentioning how some chemicals alter the surface tension which I don’t know much about so I’m not sure how much of an effect this has, but I have definitely had both Sprite and Mtn Dew explode (fizz over) on me if I shake or drop the bottle or can before opening it.
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