What is this asymptotic equivalence called?

Question

Define $$f\equiv g \iff \exists c,N\quad\forall n>N \quad |f(n)-g(n)|<c$$ What is this called?

It is not the same as $$f\sim g \iff \forall \epsilon>0 \quad \exists N \quad \forall n>N \quad |\frac{f(n)}{g(n)} -1|<\epsilon$$

Answer 1

Well, you can write it as $$f(n)=g(n)+O(1).$$ It does not have a special name or notation of its own.