ag.algebraic geometry - What is the link between sections and sections? (schemes)

Sections to the morphism $X to S$ are more or less $S$-rational points of $X$: if for example $S = Spec(R)$ and $X = Spec(R[x_1, dots, x_n]/(f_1, dots, f_m))$ with polynomials $f_1, dots, f_m in R[x_1, dots, x_n]$, then sections to $X to S$ correspond to points $(a_1, dots, a_n) in R^n$ with $f_i(a_1, dots, a_n) = 0$ for all $i$.

On the other hand, the elements of $mathcal{O}_X(U)$ can be seen as holomorphic functions on $U$.

So the one kind of sections can be seen as "points" of the geometric object, the others can be seen as "functions" on the geometric object.