Detect float type from label

It's straightforward to achieve your objective by employing the cleveref package and its \namecref macro.

If you need to upppercase the first letters in figure and table, load the cleveref package with the option capitalise. (capitalize works too.)

\documentclass{article}
\usepackage[colorlinks]{hyperref}
\usepackage[nameinlink,noabbrev]{cleveref}
\begin{document}
\begin{figure}[h]\caption{Hello}\label{fig:h}\end{figure}
\begin{table}[h]\caption{Goodbye}\label{tab:g}\end{table}

\Cref{fig:h} shows that \dots

The \namecref{fig:h} shows that \dots

\Cref{tab:g} show that \dots

The \namecref{tab:g} demonstrates that \dots
\end{document}

The following inserts the reference type as the fifth, unused element in the components written with every \label:

\documentclass{article}

\usepackage{hyperref,etoolbox}

\makeatletter
\def\strip@@period#1.#2\@nil{#1}
\def\@@currentHref{\expandafter\strip@@period\@currentHref\@nil}
\newcommand{\@@fifthoffive}[5]{%
  \@ifundefined{type@name@#5}
    {#5}
    {\csname type@name@#5\endcsname}%
}
\newcommand{\settyperef}[2]{\@namedef{type@name@#1}{#2}}
\newcommand{\typeref}[1]{%
  \HyRef@StarSetRef{#1}\@@fifthoffive
}%
\AtBeginDocument{
  % \patchcmd{<cmd>}{<search>}{<replace>}{<success>}{<failure>}
  \patchcmd{\label}{{\@currentHref}{}}{{\@currentHref}{\@@currentHref}}{}{}
}
\makeatother

\begin{document}

\begin{figure}
  \caption{A figure caption}
  \label{fig:figure}
\end{figure}

See \autoref{fig:figure}. It is a \typeref{fig:figure}.

\settyperef{figure}{FiGuRe}

See \autoref{fig:figure}. It is a \typeref{fig:figure}.

\end{document}

\settyperef{<type>}{<output>} allows you to format what the output should look like.