How to change the numbering for different figures?

Question

Let's say I have two standard figures and two supplementary figures. If I change the name of figure using \renewcommand{\figurename} the figure counter will still count all figures continuously (i.e. Fig 1, Fig 2, Supp Fig 3, Supp Fig 4 – see code below). How can I reset the figure counter so it will count standard figures separately from supplementary figures?

\documentclass[]{article}
\usepackage[footnotesize]{caption}
\begin{document}
\begin{figure}[ht]
\caption{}
\end{figure}
\begin{figure}[ht]
\caption{}
\end{figure}
\begin{figure}[ht]
\renewcommand{\figurename}{Supplementary Figure}
\caption{}
\end{figure}
\begin{figure}[ht]
\renewcommand{\figurename}{Supplementary Figure}
\caption{}
\end{figure}
\end{document}

Answer 1

In preamble,

\usepackage{newfloat}
\DeclareFloatingEnvironment[name={Supplementary Figure}]{suppfigure}

In text,

\begin{suppfigure}
\caption{...}
\end{suppfigure}

If you use old versions of caption package, there is no newfloat package, then use caption package and \DeclareCaptionType command instead.

Answer 2

You can use \setcounter{figure}{0} to reset the figure counter. However, as noted by lockstep in the comments, this will cause the number of the next "normal" figure to be wrong, as demonstrated in the example below, which has two Figure 2.

Another option is to define a new float style with the float package.

\documentclass[]{article}
\usepackage{float}
\usepackage[footnotesize]{caption}

\newfloat{suppfig}{tbh}{losf}
\floatname{suppfig}{Supplementary Figure}
\begin{document}
\begin{figure}[ht]
\caption{}
\end{figure}
\begin{figure}[ht]
\caption{}
\end{figure}
\setcounter{figure}{0}
\begin{figure}[htb!]
\renewcommand{\figurename}{Supplementary Figure}
\caption{}
\end{figure}
\begin{figure}[htb!]
\caption{}
\end{figure}
\begin{suppfig}[htb!]
\caption{}
\end{suppfig}
\begin{suppfig}[hb!]
\caption{}
\end{suppfig}
\end{document}