Using an image as a table

You must differentiate between the table float environment and the tabular environment.

tabular is for creating the table structure and can basically be used everywhere. table is for creating floats which hold a logical table, i.e. it is a container, mostly for tabulars, but could contain anything (except page breaks etc.). LaTeX then places the content at the best position, e.g. at the top of the next page.

You can include your image as a table using the following (example) code:

\begin{table}
  \centering % to have it centered
  \caption{The table caption you like}\label{tab:somelabel}
  \includegraphics[width=.95\textwidth]{yourimagefile}
\end{table}

This includes the image with 95% of the text width. Different widths are possible, of course. I just wanted to show how to use a LaTeX length together with a factor.

If you want the caption below the table, simply move \caption below \includegraphics. Please note that the caption skip might not be correct for top-side captions. The KOMA classes provide an option tablecaptionabove (or so) to fix this. See How to force table caption on top? for more.

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The same principle is true for figures where figure is the floating container and \includegraphics (or another image inclusion macro) is the content producing macro which can also be used outside figure. You can use this to declare a tabular as a logical figure. Its cells can of course also include \includegraphics macros. This is often used to lay out multiple images (with or without some extra text) as one figure.

\begin{figure}
  \centering % to have it centered
  \begin{tabular}{ll}
      A logical & figure \\
      with a & tabular structure \\
  \end{tabular}
  \caption{The figure caption you like}\label{fig:somelabel}
\end{table}

It's even possible to have multiple \caption in different cells, but for this there are now specialized packages as mentioned in e.g. Table of images with captions.

You don't have to do anything. The table environment doesn't have to contain a tabular environment.

\documentclass[12pt]{scrartcl}
\begin{document}
\listoftables
\begin{table}
Whatever you want, e.g.\ an image.
\caption{My first table}
\end{table}
\end{document}