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The <placement>=<distance> of <node>.<anchor> syntax only works with the advanced positioning library. The parts

• distance and
• of <node>.<anchor> are both optional as
  • .<anchor> is too.

Depending of <placement> the anchor key of the to-be-placed node is internally set according to the following table. The third column shows the default <anchor> if the .<anchor> part is omitted. (The sans-positioning <placement> key is just a better-to-comprehend version of the anchor key.)

 <placement>    anchor        .<anchor>
——————————————————————————————————————————
 above          south         .south
 left           east          .west
 below          north         .south
 right          west          .east
––––––––––––––––––––––––––––––––––––––––––
 base left      base east     .base west
 base right     base west     .base east
 mid left       mid east      .mid west
 mid right      mid west      .mid east
––––––––––––––––––––––––––––––––––––––––––
 above left     south west    .north east
 above right    south east    .north west
 below left     north west    .south east
 below right    north east    .south west

If no <distance> is given, the value of node distance is taken.

Note that for the four bottom ones the <distance> part can consist of <vertical distance> and <horizontal distance>. (The same is true for the node distance key that is enhanced by the positioning library also.)

The on grid option sets both anchors (the one of the to-be-placed node as well as the referenced .<anchor>) to .center so that the nodes are placed in a grid.

The topics covered by the last two paragraphs are further explained in the PGF manual in section 16.5.3 “Advanced Placement Options”, pp. 185ff.

Example (with positioning library)

Code

\documentclass[tikz,border=2pt]{standalone}
\usetikzlibrary{positioning}
\begin{document}
\begin{tikzpicture}[nodes=draw]
  \node (node1) at (0, 0) {Node 1};
  \node[below=5pt of node1] (node2) {Node 2};
\end{tikzpicture}
\end{document}

Example (without positioning library)

Without the positioning library this can be achieved by combining

• the old <placement>=<distance> and
• the at=<node>.<opposite anchor> key,

where <opposite anchor> is the corresponding .<anchor> of the table above.

The correct anchor part is set without the positioning library, too.

Code

\documentclass[tikz,border=2pt]{standalone}
\begin{document}
\begin{tikzpicture}[nodes=draw]
  \node (node1) at (0, 0) {Node 1};
  \node[below=5pt,at=(node1.south)] (node2) {Node 2};
\end{tikzpicture}
\end{document}

Output

The positioning library is missing:

\usetikzlibrary{positioning}