The right of
key isn't described in the manual at all (at least I couldn't find it). In fact, those keys are deprecated. The file pgf/frontendlayer/tikz/tikz.code.tex
contains the following code:
% The following are deprecated:
\tikzoption{above of}{\tikz@of{#1}{90}}%
\tikzoption{below of}{\tikz@of{#1}{-90}}%
\tikzoption{left of}{\tikz@of{#1}{180}}%
\tikzoption{right of}{\tikz@of{#1}{0}}%
\tikzoption{above left of}{\tikz@of{#1}{135}}%
\tikzoption{below left of}{\tikz@of{#1}{-135}}%
\tikzoption{above right of}{\tikz@of{#1}{45}}%
\tikzoption{below right of}{\tikz@of{#1}{-45}}%
\def\tikz@of#1#2{%
\def\tikz@anchor{center}%
\let\tikz@do@auto@anchor=\relax%
\tikz@addtransform{%
\expandafter\tikz@extract@node@dist\tikz@node@distance and\pgf@stop%
\pgftransformshift{\pgfpointpolar{#2}{\tikz@extracted@node@distance}}}%
\def\tikz@node@at{\pgfpointanchor{#1}{center}}}
\def\tikz@extract@node@dist#1and#2\pgf@stop{%
\def\tikz@extracted@node@distance{#1}}
That is, the center of the new node is placed node distance
away from the center anchor of the old node (where only the first number in node distance
is used). You can see why this option is deprecated if you try a wide node:
\begin{tikzpicture}
\node (a) {loooooooooooooooooooooooooooooong};
\node[right of=a,font=\bfseries,blue] (b) {node b};
\end{tikzpicture}

On the other hand right=of
would measure the node distance
(defaulting to 1cm) from the east anchor of node a to the west anchor of node b:

Note that in order to use the right=of ⟨node⟩
syntax, you need to include the TikZ library positioning
via \usetikzlibrary{positioning}
.
above right of=
appears on page 192 in the last example of/tikz/swap
.