I read somewhere that if $X$ is a projective variety of general type over a number field $K$, then rational points are an analogue of entire curves $\mathbf{C}\to X^{an}$ (with $X^{an}$ the analytification of $X_{\mathbf{C}}$ for some $K\to \mathbf C$).

Rational points are algebraic points of degree $1$ on $X$ and they "correspond" to entire curves.

Naive question:

Let $m\geq 2$. What do algebraic points of degree $m$ on $X$ "correspond" to?