In the Feynman lectures, it is stated
Also, I should say that $S$ is not really called the ‘action’ by the most precise and pedantic people. It is called ‘Hamilton´s first principal function.’ Now I hate to give a lecture on ‘the-principle-of-least-Hamilton’s-first-principal-function.’ So I call it ‘the action.’ Also, more and more people are calling it the action. You see, historically something else which is not quite as useful was called the action, but I think it’s more sensible to change to a newer definition. So now you too will call the new function the action, and pretty soon everybody will call it by that simple name.
Certainly Feynman is right is saying that pretty soon everybody will refer to this quantity by the action, as I am completely unfamiliar with this historical terminology controversy.
Does anyone know what in particular he was referring to?