If you do, from a terminal window,
latexdef subsection subsubsection`
you will get the standard definition for \subsection and \subsubsection
\subsection:
\long macro:->\@startsection {subsection}{2}{\z@ }{-3.25ex\@plus -1ex \@minus -.2ex}{1.5ex \@plus .2ex}{\normalfont \large \bfseries }
\subsubsection:
\long macro:->@startsection {subsubsection}{3}{\z@ }{-3.25ex@plus -1ex @minus -.2ex}{1.5ex @plus .2ex}{\normalfont \normalsize \bfseries }
so you see that the simple difference is the font size. OK, how can you easily fix it? In two ways, neither of which relying on using \subsubsection instead of \subsection.
Method 1: sectsty
\documentclass{article}
\usepackage{sectsty}
\subsectionfont{\normalsize}
\begin{document}
\section{Section}
\subsection{I Want This Numbered as a Subsection}
\section{Other Section}
\subsection{I Don't Want This Zero in the Middle}
\subsection{For Example, This Should be 2.1''} \section{Third Section} \subsection{This Should Be Numbered3.1''}
\subsection{I Don't Want This ``0'' for a Non-Existent Subsection}
\end{document}
There are two innocuous warnings.
Method 2: etoolbox
\documentclass{article}
\usepackage{etoolbox}
\patchcmd{\subsection}{\large}{\normalsize}{}{}
\begin{document}
\section{Section}
\subsection{I Want This Numbered as a Subsection}
\section{Other Section}
\subsection{I Don't Want This Zero in the Middle}
\subsection{For Example, This Should be 2.1''} \section{Third Section} \subsection{This Should Be Numbered3.1''}
\subsection{I Don't Want This ``0'' for a Non-Existent Subsection}
\end{document}
Output with either method

titlesecto modify the style of\subsectionto meet your typographical preference. Here on this site you can find plenty such examples. – Jinwen Feb 27 '22 at 08:58\subsubsections that for all intents and purposes work like\subsections, except for the heading's font size. Am I reading this right? If this is true, it would open up a different (simpler) kind of solutions. (f.i. you could do what @Jinwen suggested: edit the typographical looks of\subsection) – marquinho Feb 27 '22 at 08:58