This seems be what you're after...
Using the caption package you can modify captions by removing the label separator. Additionally, I've redefined \caption so you only need to specify a single (mandatory) argument. (Edit: Moved redefinition to after \begin{document}.) oldcaption gives the default behavior of caption.
\documentclass{article}
\usepackage{caption}% http://ctan.org/pkg/caption
\usepackage{lipsum}% http://ctan.org/pkg/lipsum
\usepackage[demo]{graphicx}% http://ctan.org/pkg/graphicx
\usepackage{letltxmacro}% http://ctan.org/pkg/letltxmacro
\DeclareCaptionTextFormat{none}{} \captionsetup[figure]{labelsep=none,textformat=none}
\begin{document}
\tableofcontents
\listoffigures
\section{First section}
\lipsum[1]
\begin{figure}[ht]
\centering \includegraphics{image1}
\caption[Unused first legend]{This is a first legend}
\end{figure}
\lipsum[2]
\begin{table}[ht]
\caption[a, b, and c]{The first $3$ letters of the alphabet}
\centering
\begin{tabular}{lll}
\hline
a & b & c \\
\hline
\end{tabular}
\end{table}
\lipsum[1]
\begin{figure}[ht]
\centering \includegraphics{image2}
\caption[Unused second legend]{This is a second legend}
\end{figure}
\lipsum[3]
\end{document}

lipsum provides filler text, while the demo option to graphicx is just meant for this MWE example, since it doesn't have images included. Captions are just typeset as Figure <num>, while the actual figure caption is included in the "List of Figures".