Some more information:
QUAD is the abbreviation of quadrat. It comes from quadratus in Latin (Merriam-Webster).
\qquad are macros defined by (La)TeX kernel:
For TeXicians, the unit “em” is one of the font dimensions. Say,
\fontdimen6 of a font in TeX. It originally means the width of capital letter M in a font (see Wikipedia), but it is not always true in practice.
The font dimensions in TeX and the
\fontdimen command is described in “Appendix F: Font Tables” in The TeXbook, and “Appendix F: Font Metric Information” in The METAFONTbook.
You can define a macro equivalent to
\quad like this:
and of course a