It's vice versa -- stearic acid, a fatty acid, can be made from stearin, a fat.
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But the OP asked about "stearine" with an "E" on the end. The word "stearine" with an "E" may indeed be a synonym for stearic acid, not stearin, but the similarity to "stearin" without the "E" is confusing. I'd be real careful to confirm which chemical that you've got before assuming you have one or the other.
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Tallow, lard, palm and other fats can be separated fairly easily into "stearin" and "olein" by cooling the melted fat slowly until some it solidifies. The solid part of the fat -- the stearin -- is filtered out of the liquid part of the fat -- the olein. Like any other triglyceride fat, stearin (or olein) creates glycerin when it is saponified.
Stearic acid is made by further processing the stearin to break the fat molecules apart into glycerin and fatty acid molecules. The glycerin is removed and the fatty acids that remain are either sold as commercial grade stearic acid, which is a mix of mostly stearic and palmitic acids, or further purified. Stearic acid adds no glycerin when it saponifies.
Stearin will saponify slowly just like any normal soaping fat, while stearic acid saponifies very quickly, just like any a fatty acid.