\documentclass{article}
\newcommand{\foo}{}
\renewcommand*{\foo}[1]{#10}
\providecommand{\foo}[1][default]{#11}
\newenvironment*{baz}{START}{STOP}
\renewenvironment{baz}[1]{HEAD of #12:}{TAIL}
\renewenvironment*{baz}[1][default]{BEGINNING of #12:}{END}
\begin{document}
\foo{TeX}  % -> TeX0
\begin{baz} tex \end{baz}  % -> BEGINNING of default2:tex END
\end{document}