what does [length] after a `\\` mark mean

Question

what does \[length] mean? like this:

\documentclass{article}
\begin{document}
mmmmm\\[-0.33em]
mmmmm

mmmmm

\hspace{-0.33em}mmmmm
\end{document}

why are these do not render the same?

Answer 1

To begin with, LaTeX commands can take both required and optional arguments. Required arguments are (generally) enclosed by curly braces, while optional arguments are enclosed by square brackets.

Next, if the string

mmmmm\\[-0.33em]

occurs inside an array or a tabular-like environment, the sub-string \\ is the instruction to insert a line break and [-0.33em] represents an optional argument to the \\ instruction. If the argument, which is supposed to be a length, is a positive, additional vertical whitespace -- in the amount of that argument -- will be inserted; it it's negative, that amount will be subtracted from the default amount of vertical space that's inserted by \\.

(Aside: If you use \\ outside of array and tabular-like environments, it's quite likely that you're doing something wrong...)

In contrast, \hspace is a text-mode command that serves to insert or subtract horizontal space. Incidentally, to LaTeX, \hspace{0pt} is not the same as "doing nothing" -- inserting "zero-length whitespace" can have significant and (if used correctly) very handy use cases.

In short, there's no reason to believe that \\[-0.33em] and \hspace{-0.33em} would, let alone should, produce the same outcome.