Let $(X, J)$ be an almost complex manifold and $u: C \to X$ be J holomorphic curve. I confuse the following three definitions, are they equivalent?
$u$ is simple if $u$ is not multiple cover, i.e. $u$ cannot factorize as $u=v \circ \varphi $, where $\varphi: C \to C'$ is $k$-fold branch cover with $k \ge 2$, and $v: C' \to X$ is holomorphic curve such that $v$ is embedded except at a finite set.
$u$ is somewhere injective if $u^{-1}\{u(z)\} = z $ for some $z \in C$.
$u$ is immersion.
(1) and (2) are equivalent, the proof is not obvious though (the rough idea is obvious). There is a nice blog post of Chris Wendl (called "Somewhere injective vs. multiply covered"), giving a general proof. Otherwise, for closed curves, see the two proofs of Proposition 2.5.1 in McDuff-Salamon's big book "J-holomorphic Curves and Symplectic Topology".
Now (2) and (3) are easily not the same, the curve can be singular... did you try looking at examples?