No. It is not just that a-b=c is equivalent to b+c=a. The point is also that you can use this to find a difference, but using what you know about finding sums. And this is clearly different for 4 digits than for 1 digit. It gives a more efficient and natural algorithm for multidigit subtraction than the grotesque method typically taught in American schools.
No, it's the same for 4 digits and 1 digit. That's a major point in mathematics: concepts aren't different, don't change or fail to apply because you use different numbers. It has to work every time or it's wrong.
If you're referring to subtraction with regrouping, I'm not sure why you're calling the standard algorithm
grotesque. However, I do know that many folks without a solid understanding of mathematics and how its pieces fit together often mistakenly believe that the standard methods are somehow bad and should not be taught. There is a LOT of misinformation out there. I recommend reading
this paper by a mathematician from UC Berkeley. He does a good job of explaining why misunderstandings arise. He also discusses the importance of the standard algorithms and how they fit together in the broader tapestry of mathematics.
