The difference between Cosmetic and Product
When used as nouns, cosmetic means any substances applied to enhance the external color or texture of the skin, e.g. lipstick, eyeshadow, eyeliner, whereas product means a commodity offered for sale.
Cosmetic is also adjective with the meaning: imparting or improving beauty, particularly the beauty of the complexion.
check bellow for the other definitions of Cosmetic and Product
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Cosmetic as an adjective:
Imparting or improving beauty, particularly the beauty of the complexion.
Examples:
"a cosmetic preparation"
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Cosmetic as an adjective:
External or superficial; pertaining only to the surface or appearance of something.
Examples:
"Fortunately, the damage to the house was mostly cosmetic and a bit of paint covered it nicely."
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Cosmetic as a noun:
Any substances applied to enhance the external color or texture of the skin, e.g. lipstick, eyeshadow, eyeliner; makeup.
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Cosmetic as a noun:
A feature existing only on the surface.
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Product as a noun (countable, uncountable):
A commodity offered for sale.
Examples:
"That store offers a variety of products.  We've got to sell a lot of product by the end of the month."
"synonyms: merchandise wares goods"
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Product as a noun (cosmetics, uncountable):
Any preparation to be applied to the hair, skin, nails, etc.
Examples:
"Wash excess product out of your hair."
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Product as a noun (chemistry):
Anything that is produced; a result. The amount of an artifact that has been created by someone or some process. A consequence of someone's efforts or of a particular set of circumstances. A chemical substance formed as a result of a chemical reaction. A quantity obtained by multiplication of two or more numbers. Any operation or a result thereof which generalises multiplication of numbers, like the multiplicative operation in a ring, product of types or a categorical product. Any tangible or intangible good or service that is a result of a process and that is intended for delivery to a customer or end user.
Examples:
"The product of last month's quality standards committee is quite good, even though the process was flawed."
"They improve their product every year; they export most of their agricultural production."
"synonyms: endwork production output creation yield"
"Skill is the product of hours of practice.  His reaction was the product of hunger and fatigue."
"This is a product of lime and nitric acid."
"The product of 2 and 3 is 6.  The product of 2, 3, and 4 is 24."
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Product as a noun (US, slang):
Illegal drugs, especially cocaine, when viewed as a commodity.
Examples:
"I got some product here – you buying?"