Smith didn’t ‘coin’ the phrase at all. It was a well-known phrase going back to classical times (Ovid), and was widely used in the 17th and 18th centuries in both religious tracts, sermons and books, and in literary works (Shakespeare, Defoe, Voltaire and others.]
…
He used the term not in his discussion and analysis of markets (Book I and II of Wealth Of Nations), but in a discussion of the choice of export/importing versus investing in domestic businesses (Book IV of Wealth Of Nations on his critique of mercantile political economy). It had nothing to do with ‘regulating’.
…
It was a metaphor Smith used only three times and he never said “that when this invisible hand exists, when we all pursue our own interest, we end up promoting the public good, and often more effectively than if we had actually and directly intended to do so.” That is a modern construction placed on the metaphor and has next to nothing to do Adam Smith
…
The invisible hand was never in Adam Smith’s world in the form invented in mid-20th century by some economists who created the Chicago version of Adam Smith, while ignoring the Adam Smith born in Kirkcaldy, Scotland in 1723.