  Let $C$ be an isolated plane curve singularity, and $(C,l)$ be a decorated
curve. In this article we compare the equisingular deformations of $C$ and the
sandwiched singularity $X(C,l)$. We will prove that for $l \gg 0$ the functor
of equisingular deformations of $C$ and $(C,l)$ are equivalent. From this we
deduce a proof of a formula for the dimension of the equisingular stratum.
  Furthermore we will show how compute the equisingularity ideal of the curve
singularity $C$, given the minimal (good) resolution of $C$.
