Node made on label and not position tikz

I think you want something like the right figure below, left and middle figure are the result form your codes.

Command \draw just draws a path between provided coordinates, but it doesn't creates any labels for further reference. You need node or coordinate (an special kind of node) to assign labels to certain points on your canvas which can be later on used to draw lines between them or place new elements.

Your first command

\draw[thin,ball color=red] (0,0) circle(0.4ex) node(mX1){}; 

draw a red ball on coordinate (0,0) and also draws an invisible and empty node named mX1 on same coordinate. Change node (mX1) {} to node[draw] (mX1) {} to make it visible.

Second command

\draw[thin,ball color=white] (1,1) circle(0.4ex) node[left] (X1){$X_1$}; 

does something similar, it draw a white ball on (1,1) but a node called X1 is placed to the left (1cm by default) of (1,1).

Line \draw (X1)--(mX1); goes form X1 border to mX1 border. And although X1 node is at origin, mX1 is not on white ball center, but to the left of it.

Proposed solution

\node[circle, very thin, ball color=red!50, minimum size=0.8ex, inner sep=0pt] (mX1) at (0,0) {}; \node[circle, very thin, ball color=white!50, minimum size=0.8ex, label=left:$X_1$, inner sep=0pt] (X1) at (1,1) {}; 

draws balls as circular nodes. This way X1 and mX1 make reference to balls center. And label X_1 is set as a label of second node. minimum size=0.8ex fixes ball diamenter if inner sep=0pt. This way line between nodes borders shows no separation from them.

\documentclass[border=2mm]{standalone} \usepackage{tikz} \begin{document} \begin{tikzpicture} \draw[help lines] (0,0) grid (1,1); \draw[thin,ball color=red] (0,0) circle(0.4ex) node(mX1){}; \draw[thin,ball color=white] (1,1) circle(0.4ex) node[left] (X1){$X_1$}; \draw (X1)--(mX1); \end{tikzpicture} \begin{tikzpicture} \draw[help lines] (0,0) grid (1,1); \draw[very thin,ball color=red!50] (0,0) circle(0.4ex) node(mX1){}; \draw[thin,ball color=white,label=X1] (1,1) circle(0.4ex) node{$X_1$}; \draw (X1)--(mX1); \end{tikzpicture} \begin{tikzpicture} \draw[help lines] (0,0) grid (1,1); \node[circle, very thin, ball color=red!50, minimum size=0.8ex, inner sep=0pt] (mX1) at (0,0) {}; \node[circle, very thin, ball color=white!50, minimum size=0.8ex, label=left:$X_1$, inner sep=0pt] (X1) at (1,1) {}; \draw (X1)--(mX1); \end{tikzpicture} \end{document}