For many symbols it’s just that the purpose is different. Consider the set minus: what you want there isn’t a backslash. You really want a “set minus” – which just happens to be displayed (sometimes) identically to a backslash. But it’s still fundamentally different.
Now, which of the two LaTeX codes is more readable:
\mathcal{F} \backslash \{ 0 \}
% or
\mathcal{F} \setminus \{ 0 \}
If the two are really identical (which I don’t believe since as Carsten points out there’s always the issue of spacing in math mode) one can simply be defined in terms of the other – e.g.:
\newcommand*\setminus{\backslash}
No harm in that. This still makes the usage more readable (see above) and the macro can be exchanged very quickly if you decide that the symbol should be displayed differently. For example, consider that the set minus is actually often written like a normal minus instead of like a backslash. If you have used the \backslash command, you now need to change all occurrences of that in your document.
If you have used a dedicated command then you only need to redefine that:
\newcommand*\setminus{\ensuremath{{}-{}}}
In practice, I redefine aliases for almost all macros that I use to fit my current use-case.
Best Answer
The correct syntax is
The
\calcommand was used in LaTeX 2.09 and has been obsolete since the release of LaTeX2e (1992). It worked as a font change declaration rather than a command with argument, so the right way would have beenwhich is quite confusing.