[REVISED VERSION aimed at making the MWE more realistic]
I have two related figures of different width that are drawn in the tikzpicture environment using pgfplots and the related axis environment. The pictures are currently drawn for a beamer document class, thus being able to exploit the \only command to establish an order for the various operations. In particular, such order is needed because each of the picture makes use of some information which is extracted from the other picture at the previous frame: this is what establishes a link between the pictures. In particular, each picture makes use of some coordinate component extracted from the previous picture, and at least some of such coordinates are determined via the intersections library.
All this works perfectly fine in beamer, thanks to the \only command.
Is there a relatively easy way to reproduce the same mechanism in a non-beamer document class such as article?
I have already consulted a number of related Q&A (such as this and of course this), but I cannot arrive to any solution starting from there. I think my coding skills are just insufficient to make it on my own. Additionally, I have consulted the animate package documentation, but its possible solutions (if any) to the present problem appear to be very convoluted. Finally, I have considered externalizing and exporting to pdf each picture to then include their final frame where needed. Unfortunately, the heterogenous widths of pictures make this solution scarcely viable when one has to produce and include many pictures.
I hereby provide a revised MWE and the last frame of the resulting output. 
\documentclass{beamer}
\usepackage[mode=buildnew]{standalone}
\usepackage{tikz,pgfplots}
\usetikzlibrary{intersections}
% Coordinate extraction
% from: https://tex.stackexchange.com/questions/420498/extract-convert-store-and-reuse-x-y-coordinate-components
\newlength{\lenx}
\newlength{\plotwidth}
\newlength{\leny}
\newlength{\plotheight}
\newcommand{\getvalue}[1]{\pgfkeysvalueof{/pgfplots/#1}}
\newcommand{\Getxycoords}[3]% #1 = node name, #2 x coordinate, #2 y coordinate
{\pgfplotsextra{%
\pgfextractx{\lenx}{\pgfpointdiff{\pgfplotspointaxisxy{0}{0}}{\pgfpointanchor{#1}{center}}}%
\pgfextractx{\plotwidth}{\pgfpointdiff{\pgfplotspointaxisxy{\getvalue{xmin}}{0}}%
{\pgfplotspointaxisxy{\getvalue{xmax}}{0}}}%
\pgfextracty{\leny}{\pgfpointdiff{\pgfplotspointaxisxy{0}{0}}{\pgfpointanchor{#1}{center}}}%
\pgfextracty{\plotheight}{\pgfpointdiff{\pgfplotspointaxisxy{0}{\getvalue{ymin}}}%
{\pgfplotspointaxisxy{0}{\getvalue{ymax}}}}%
\pgfmathsetmacro{\myx}{\lenx*(\getvalue{xmax}-\getvalue{xmin})/\plotwidth}%
\pgfmathsetmacro{\myy}{\leny*(\getvalue{ymax}-\getvalue{ymin})/\plotheight}%
\xdef#2{\myx}%
\xdef#3{\myy}%
% \typeout{\myx,\myy} <- for debugging
}%
}
\begin{document}
\begin{frame}
\centering
\begin{tikzpicture}[baseline=(current bounding box.north),trim axis left,trim axis right]
\begin{axis}[scale=0.6,clip=false,ytick={0}]
\addplot [name path=f,smooth,domain=-20:20] {1+0.5*x} node [anchor=north,yshift=-2mm] {$f(x)$};
\addplot [name path=h,smooth,domain=-20:20] {8+1*x} node [anchor=south,yshift=-2mm] {$h(x)$};
\only<2->{
\path [name intersections={of=f and h,by={A}}] node [anchor=south] at (A) {$A$}; %Assign point A
\Getxycoords{A}{\Ax}{\Ay};
\draw [fill=red] (A) circle (2pt);
}
\only<4->{
\node (C) at (axis cs:{(\By-1)/0.5},\By) {}; %Get point C given point B
\Getxycoords{C}{\Cx}{\Cy};
\draw [fill=red] (C) circle (2pt) node [anchor=south] {C};
\draw [dashed] (axis cs:\Cx,\pgfkeysvalueof{/pgfplots/ymin}) -- (C) -- (axis cs:\pgfkeysvalueof{/pgfplots/xmin},\Cy) node [anchor=east] {$y$-component of $C$};
}
\end{axis}
\end{tikzpicture}
\begin{tikzpicture}[baseline=(current bounding box.north),trim axis left,trim axis right]
\begin{axis}[scale=0.6,clip=true,ytick={0}]
\addplot [name path=g,smooth,domain=-20:20] {1+0.6*x} node [anchor=north,yshift=-2mm] {$g(x)$};
\only<3->{
\node (B) at (axis cs:\Ax,{1+0.6*\Ax}) {}; %Get point B given point A
\Getxycoords{B}{\Bx}{\By};
\draw [fill=red] (B) circle (2pt) node [anchor=south] {B};
}
\end{axis}
\end{tikzpicture}
\end{frame}
\end{document}
animatepackage – samcarter_is_at_topanswers.xyz Mar 21 '18 at 10:02tikzpicture, it is straightforward to align them horizontally (as strictly needed) via thetrim axiscommand. Instead, horizontal alignment has to be done manually once you include the pictures, due to the fact that the pictures have different width. Since I have many pictures, I cannot take this road. Also, I am having troubles changing thebeamerfont intikzpictureto the same serif font used inarticle. – Brocardo Reis Mar 23 '18 at 14:21\usefonttheme{serif}(and depending an which document class you use for your article, change the size). Both plots you showed us, have the same width. – samcarter_is_at_topanswers.xyz Mar 23 '18 at 14:28\usefonttheme{serif}, that is what I have used. Such command works smoothly when the pictures at stake are not externalized via theexternallibrary, which is instead what I have actually used so far. – Brocardo Reis Mar 23 '18 at 14:35standalone, this means that the two graphs would have to be printed in a single file, so that its inclusion won't cause problems with horizontal alignment. – Brocardo Reis Mar 23 '18 at 17:12