Shinola was a brand of shoe polish previously manufactured in the USA. The alliteration and the fact that the two commodities in the phrase could possibly be confused is the derivation. The distinction is well made; only one of them would be good to apply to your shoes and only particularly dim people could be expected to muddle them up. Of course, outside America, most people don't know Shinola from anything at all, as they've never heard of it. Even in America it would probably not be widely remembered but for this phrase.
- When someone doesn't know anything about what they should know something about, they don't know sh#t from shinola.
- Someone possessing poor judgment or knowledge doesn't know sh#t from shinola.