\documentclass{article}
\usepackage{amsthm}
\usepackage{color}

\newtheoremstyle{redPlain}  {\bigskipamount}
                            {\bigskipamount}
                            {\itshape}
                            {0pt}
                            {\color[cmyk]{0,1.00,0.65,0.34}\bfseries}
                            {:}
                            {1em}
                            {\thmname{#1}\thmnumber{ #2}\thmnote{ (#3)}}
\theoremstyle{redPlain}
\newtheorem*{starred}{Starred}
\newtheorem{normal}{Normal}
\newtheorem{normalshared}[normal]{Normal And Shared}
\theoremstyle{plain}
\newtheorem{within}{Within}[section]
\newtheorem{withinshared}[within]{Within And Shared}

\begin{document}

\section{A section}
\begin{starred}[Note]
    An starred theorem
\end{starred}
\begin{normal}
    A normal theorem
\end{normal}
\begin{normalshared}[Note]
    A normal theorem, with shared counter.
\end{normalshared}
\begin{within}
    A theorem numbered within sections
\end{within}
\begin{withinshared}[Note]
    A theorem with counter shared with a theorem numbered within sections
\end{withinshared}
\section{Another section}
\begin{starred}
    An starred theorem
\end{starred}
\begin{normal}
    A normal theorem
\end{normal}
\begin{normalshared}
    A normal theorem, with shared counter.
\end{normalshared}
\begin{within}
    A theorem numbered within sections
\end{within}
\begin{withinshared}\label{T:1}
    A theorem with counter shared with a theorem numbered within sections
\end{withinshared}
\end{document}
