You might have lighted on what's commonly called Moore's 'paradox of analysis' (after GE Moore). The paradox centres on definitions.
Let's take a triangle as a thing to be defined. It is standard to assume that what we want from a definition is that it be correct and also informative. Suppose you don't know what a triangle is (just bear with me !). I might say :
'A triangle is a three-sided plane figure with three internal angles'.
That's correct enough. It also tells you something; it is informative.
But now a problem sneaks in. If the definition is right, then (1) 'triangle' and (2)'three-sided plane figure with three internal angles' pick out the same concept. They refer to exactly the same thing. If that's so, however, we should be able to interchange the expressions - whenever one expression (1) is appropriate to use then so expression (2). This proves awkward for informativeness, however, because if we switch (1) for (2) in :
'A triangle (1) is a (2) three-sided plane figure with three internal angles'
we get :
'A triangle is a triangle'.
This is completely uninformative. To preserve informativeness we seem stuck with saying that (1) and (2) are not interchangeable. If they are not, then we get what may be your idea that the definition has 'introduced a new being' or said another way that a triangle 'is different from itself'.
I've tried to be helpful here. If I've misunderstood your problem, then I apologise. I don't btw know how best to deal with Moore's paradox of analysis. Perhaps we just have to accept it and it can't be punctured. Most philosophers are unwilling to leave it at that; and they may well be right. But I've said all I can.