International Nomenclature of Cosmetic Ingredients, which sets out how our ingredients should be named on products or through suppliers. The INCI should be the same for products all around the world, and the intention is to make it clear what we are getting in our products.
A few examples...
Water - INCI Water (Aqua)
Vitamin E - INCI Tocopherol
Shea butter - INCI Butyrospermum Parkii (Shea Butter)
Jojoba oil - INCI Simmondsia Chinensis (Jojoba) Seed Oil
It's a good thing to know the INCI names of the ingredients so you aren't buying the same product through different suppliers. For instance, the INCI name for Croda's Incroquat BTMS-25 is the same as Rita BTMS-225 - both are behentrimonium methosulfate (and) cetearyl alcohol. This isn't to say they are the same product: You might have 25% behentrimonium methosulfate in one and 50% in the other, but at least you know they have the same ingredients. (As an aside, both BTMS-25 and BTMS-225 are listed as having 25% behentrimonium methosulfate.)
Anyone selling a cosmetic product should be using the INCI names. If someone is selling a product with tea tree essential oil, they should be listing it as Melaleuca Alternifolia (Tea Tree) Leaf Oil not tea tree essential oil. Some people might list things like this to make it easier to read - olive oil (Olea Europaea (Olive) Fruit Oil) - and others might just use the INCI name.
Check out the Cosmetics Info site for more information on INCI names. I wouldn't trust the Wikipedia site to which I link above for your INCI names as they have emulsifying wax listed as cetyl alcohol for the INCI name, which is really really wrong!
Substitutions: Reading INCI names
Point of Interest: Reading INCI names