The word cola derives from the Kola nut, which is used in drinks like Coke and Pepsi to ad flavor and caffeine. To the extend that people use cola fully interchangeably with soda or pop is a bit of a misnomer, and must be a regional thing because I don't think I've ever heard something like 7-Up, Sprite, or Fanta referred to as a cola.

Soda and pop are both different words for soft drinks (as in not hard/alcoholic drinks) that are typically any sweetened, carbonated beverage. Both Coca-cola and Pepsi-cola are soft drinks, but many soft drinks are not cola drinks.

Interestingly enough, "soda", as a word referring to beverages, comes from sodium bicarbonate, which used to be called soda in several forms and is still called baking soda in the US at least. Sodium salts used to be used in carbonated water to reduce the acidity. It isn't needed or much used anymore, but old formulas may still include it. The name stuck anyway.