Algebraic term for when you get the same result with different binary operations? I suspect that this will be a simple question. 
Given that subtraction is frequently defined as $A - B = A + (-B)$, we have a circumstance where it appears that $2$ different binary operations can produce the same result (at least under specific circumstances).
Yet, not all of the properties of addition can be found in subtraction (e.g. commutative property). Something similar could be stated for multiplication and division.
So, assuming that what I have written is at least informally valid, then what is the mathematical term used to reference this observation?
I would like to read more on the matter. I have tried to think of everyday analogies that model this idea, but it seems that I lack the creativity. 

"2  different binary operations can produce the same result (at least under specific circumstances)"
Yes, and don't we also have that situation with the following? 
$$ \left(2 + 2 \right) = \left(2 \cdot 2 \right)$$
We could begin with the equation ...
$$ \left(h + k \right) = \left(m \cdot n \right)$$
... and then specify that our specific circumstance is that we plug in the value 2 for each of the four variables h, k, m, and n.
The challenge for you is to impose stricter requirements on circumstances, and then use your new idea to pose a new question, unless you or somebody else can find a better answer to the question that you actually asked.
Now, one final observation might be helpful, although I warn you that it is childishly simple:
$$ (A - C) + (C - B) = (A - B)$$
If C = 0, then we have:
$$ (A - C) = A$$
and
$$ (C - B) = (-B)$$
As Biff from "Back to the Future" might say, I will now make like a tree, and get out of here.
