$\phi$-torsion of a group

Question

Let $\phi:G\to G$ be an endomorphism of an abelian group $G$. If $\phi$ is defined by $g\mapsto g^n$, then I already know that $G[\phi]:=G[n]=$ $n$-torsion of $G=\ker(\phi)$. But if $\phi$ is a general endomorphism, then is it still true that (the $\phi$ torsion of $G$) $G[\phi]:=\ker(\phi)$? I saw this notation in the context of Selmer group of an isogeny $\phi$.