How can I force the pgfplots coordinate system and the tikz coordinate system to match and why do they not match by default?

Question

I plot a function with pgfplots and want to combine it with some simple \draw commands from tikz. But to my suprise the coordinate systems seem not to match. The rectangle drawn ranges from x=-10 up to x=10 and from y=0 up to y=1 which as well are the min and max values of the function drawn BUT they do not fit.

How can I force the pgfplots coordinate system and the tikz coordinate system to match and (if somebody knows) what is the problem here?

\documentclass[border=3mm]{standalone}
\usepackage{pgfplots}
\usepackage{tikz}
\begin{document}

\begin{tikzpicture}[domain=-10:10]

    \begin{axis}[axis lines=none]
        \addplot {exp(x)/(1+exp(x))};
    \end{axis}
    \draw[thick] (-10,0) rectangle (10,1);

\end{tikzpicture}

\end{document}

Answer 1

Making the example work:

The answer is to use a special coordinate system called "axis cs" (see the comment given by percusse above)

\documentclass[border=3mm]{standalone}
\usepackage{pgfplots}
\usepackage{tikz}

\begin{document}
\thispagestyle{empty}

\begin{tikzpicture}[domain=-10:10]
    \begin{axis}[axis lines=none]
        \addplot {exp(x)/(1+exp(x))};
        \draw[thick] (axis cs: -10,0) rectangle (axis cs: 10,1);        
    \end{axis}
\end{tikzpicture}

\end{document}

Concerning the sub-question "why is there a difference and which?"

First, let me stress: yes, there is a significant difference in the coordinate systems. And: yes, that is fully intentional; in fact: it is dictated by the different use-cases. Typically, a plot is about data visualization: it attempts to map data coordinates into visualization coordinates in a way which "makes good use of the available space". This requires rescaling of the data. Rescaling, in turn, means to use a different coordinate system. And pgfplots tries hard to hide all that complexity: with pgfplots, you simply provide the data and the result size (as width or height) and pgfplots does the rest.

Occasionally, one wants to combine both to some extend. Your use-case appears to be the desire to annotate the visualization, i.e. to draw some custom line.

Solutions are to use extra y tick combined with grid lines or to simply draw a line. If you draw a line, you place the drawing instruction inside of the axis and use (axis cs:-10,0) rectangle (axis cs:10,1) to identify the points inside of the "axis coordinate system".

Note that there is also a different use-case which is NOT data visualization. Occasionally, one wants to draw a graphical element, and the fact that its corners are identified by some coordinates has nothing to do with "visualize this data". Such applications imply to use the very same coordinate system for any TikZ instruction and for any pgfplots instruction. This is possible and is subject of a section of the pgfplots manual (called "TikZ Interoperability"). From my point of view, this is a relatively rare use-case.

The typical use-case is to enrich a data visualization by means of some drawing elements, i.e. the first one. Pgfplots supports this by means of the additional coordinate systems (there are a couple of further coordinate systems). It also plugs into the creation of circles/ellipses in order to express them by means of axis units.