\documentclass{article}
\newcount\num
\chardef\chara='3\relax
\mathchardef\mchara"1350        %= 4944
\begin{document}
\section{chardef}
% Regular counter register.
% use the CS alone means assignment
\num=10\relax
% use with \the to get the numerical value
10 = \the\num
% Chardef register.
% use the CS alone gets the character
Lambda = \chara
% Use with \the to get the numerical value
3=\the\chara
% However, on RHS of assignment, without \the
\num=\chara
3=\the\num
\section{mathchardef}
% What about mathchar ?
Sum = $\mchara$
\num=\mchara
4944=\the\num
4944=\the\mchara
% AND the perverse use of chardefs for plain number constants
\makeatletter
10000 = \the\@M
\num=\@M
10000 = \the\num
\section{fontencoding}
% Note that chardef'd chars see the current font encoding
OML: \fontencoding{OML}\selectfont\chara\fontencoding{OT1}\selectfont.
OMS: \fontencoding{OMS}\selectfont\chara\fontencoding{OT1}\selectfont.
OMX: \fontencoding{OMX}\selectfont\chara\fontencoding{OT1}\selectfont.
% But mathchardef'd chars have it effectively built in (via font family)
OML: $\fontencoding{OML}\selectfont\mchara\fontencoding{OT1}\selectfont$.
OMS: $\fontencoding{OMS}\selectfont\mchara\fontencoding{OT1}\selectfont$.
OMX: $\fontencoding{OMX}\selectfont\mchara\fontencoding{OT1}\selectfont$.
\end{document}