\vspace vs. \vskip

At any point in its processing, TeX is in some mode. There are six modes, divided in threecategories:

1. horizontal mode and restricted horizontal mode,
2. vertical mode and internal vertical mode, and
3. math mode and display math mode.

When not typesetting mathematics, TeX is in horizontal or vertical mode.Horizontal mode is typically used to make lines of text; vertical mode is typically used to stack the lines of a paragraph on top of each other.

\vskip inserts a glue in a vertical list of the lines. Therefore \vskip breaks the horizontal mode and goes to the vertical mode.

\vspace can work in horizontal mode and vertical mode.In horizontal mode \vspace 1mm is equivalent to \vadjust{\vskip 1mm \vskip 0pt} and inserts a space after the current line.In vertical mode \vspace 1mm is equivalent to \vskip 1mm \vskip 0pt

\vskip 0pt is needed so \removelastskip can not remove your vertical space.

Full definition:

\vspace : -> \@ifstar \@vspacer \@vspace 

Without * case (\vspace 1mm):

\@vspace: #1->\ifvmode \vskip #1 \vskip \z@skip \else \@bsphack \vadjust {\@restorepar \vskip #1 \vskip \z@skip }\@esphack \fi 

Note \z@skip equal to 0pt, \@bsphack is needed to save big horizontal space after period.\@esphack is needed to return big space settings.

With * case (\vspace* 1mm):

\@vspacer:#1->\ifvmode \dimen@ \prevdepth \hrule \@height \z@ \nobreak \vskip #1 \vskip \z@skip \prevdepth \dimen@ \else \@bsphack \vadjust {\@restorepar \hrule     @height \z@ \nobreak \vskip #1 \vskip \z@skip }\@esphack \fi 

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