The first thing is to know that there are spacing parameters and spacing commands; \parskip and \parindent belong to the former category, \enskip, \quad and \smallskip to the latter.
A complete list of the spacing parameters would be quite long, so let's concentrate on spacing commands.
Vertical spacing commands
\smallskip, \medskip and \bigskip leave a vertical space of some amount predefined by the class; they are particular cases of \vspace{<skip>}; if given in mid paragraph they produce a vertical space between the line where they happen to be set and the following, so they are best used between paragraphs.
\smallbreak, \medbreak and \bigbreak do almost the same, but they remove a preceding vertical space if less than what they would insert; they also terminate a paragraph and tell TeX that they mark a good point where a page break may happen.
\addvspace{<skip>} tries merging with possible other spacing of the same kind, in order to space by the maximum amount of the two (in some occasions this might not happen, the problem is quite subtle).
\vfill is equivalent to \vspace{\fill} and tells TeX to fill with white space.
The variant \vspace*{<skip>} tells TeX not to ignore the vertical spacing also if it happens to fall just after a page break; all the previous vertical spacings will in fact disappear at page breaks.
Horizontal spacing commands
\enskip, \quad, \qquad leave a horizontal space of respectively half an em, one em and two ems. The "em" is a font depending length, frequently as wide as a capital M in the current font.
\hspace{<skip>} is a general horizontal spacing command, that tells TeX to leave that amount of horizontal space.
\hspace*{<skip>} is analogous, but won't disappear at a line break.
\hfill is equivalent to \hspace{\fill}.
\, and \! leave respectively a thin space and its negative; \, can be used to fix some bad spacings caused by visually incompatible pairs of characters (an uppercase letter attached immediately after a lowercase one might be an occasion) or in cases such as D.\,E.~Knuth (that somebody prefers to D.~E.~Knuth; note that D.E.~Knuth is wrong).
What horizontal commands to use? In general it's best to rely on \quad and friends, that come from centuries of typography. When a particular application demands a different approach, the \hspace command serves the purpose.
I don't recall any spacing command that can be used both for vertical and horizontal spacing.
You mention \enspace which is, IIRC, not listed in the LaTeX manual (as aren't \smallbreak, \medbreak and \bigbreak); it's inherited from Plain TeX and is almost the same as \enskip, but technically it is a kern, rather than a skip.
The commands \, and \! have a "long version", which is to be used only in text mode (so not in formulas): \thinspace and \negthinspace. They, like \enspace, insert kerns which are different from skips in that they do not generally define a line break point (the real rule is quite complex, see the TeXbook); in particular TeX won't break a line between "D." and "E." in D.\,E.~Knuth. Moreover, kerns have only their natural width (see below for skips).
What's a <skip>?
A <skip> is a three pronged length specification:
<natural width> plus <stretching> minus <shrinking>
For example, \smallskip is equivalent to \vspace{3pt plus 1pt minus 1pt} (in the standard classes) that tells TeX to leave a vertical space of 3pt, but shrinkable up to 2pt or stretchable (optimally) up to 4pt. However, when a stretch component is present, TeX is allowed to stretch that space also beyond the stated specification, in an emergency; this happens frequently when a \pagebreak command is found when TeX has not enough material to fill correctly the current page.
The lengths can be specified in any of the legal TeX units of measure, but the stretch and shrink components can be expressed also in terms of infinite units fil, fill and filll (to be used with care). For example, if in a page TeX finds \vfill, which is the same as \vspace{0pt plus 1fill}, all the \smallskips found in the page will be 3pt wide, as the infinite component of \vfill wins.
The command \stretch can be used in this context: \stretch{<decimal number>} is equivalent to the skip specification 0pt plus <decimal number>fill, so \vspace{\stretch{2}} is equivalent to say \vfill\vfill. TeX will fill with white space proportionally to the fill components. So
\clearpage
\thispagestyle{empty}
\vspace*{\stretch{1}} % the same as `\vspace*{\fill}`
\begin{flushright}
\itshape
To my dog\\
and my cat
\end{flushright}
\vspace{\stretch{2}}
\clearpage
can be used to have a dedication placed in the page with twice as much white space below than above. Note that above one has to use \vspace* in order to avoid the spacing disappearing at the page break.
Caveat
A recent question presented a funny problem: Space generated by theorem labels (XeTeX)
It turns out that this is an undocumented feature (aka “bug that won't be fixed”): the commands \, \! \thinspace \negthinspace \enspace are defined to be
\kern<dimen>
so if they are issued in vertical mode (when TeX hasn't yet started a paragraph) they produce a vertical space rather than a horizontal one.
Be sure to issue them when a paragraph has been started; note, for example, that \item doesn't start a paragraph, nor does \begin{<theorem>} (where <theorem> stands for any environment defined with \newtheorem).
On the contrary, \quad, \qquad, \enskip and \hspace do start a paragraph if TeX is in vertical mode when it finds them.
Best Answer
One default package to display length is the package
layouts. It produces black/white images with represented lengths.For example the example below produces the following images for list-environments.
However the coloured images are probably made by packages like TikZ or PSTricks.