Whether a variable is treated as nominal or ordinal may depend on the
purpose for which the data were collected.
You mentioned 'eye color': On a driving license eye color is nominal;
if you're stopped for a traffic violation, that information helps the
police officer know whether the licence you show is really yours.
In a genetic study, eye color may be ordinal, with black, brown, grey/hazel,
and blue denoting a decreasing order of eye pigment that may be determined
by a particular set of genes. In the case of an ophthomologist who can scan for the
density of pigment cells in the iris, (s)he may record a count of pigment cells
per $mm^2$, and then eye color becomes a numerical variable.
Age measured in years is a numerical variable. But for reasons of privacy or vanity some people are more willing
to give an age category (20-35, 36-50, etc.) than an exact age. In that case
the categories essentially become an ordinal variable.
Your example of "error type" is puzzling. If there are three error types A, B and C,
and numbers such as 200, 403, etc. are for measuring something like cost
or delay, then you have two variables: error type is likely nominal (A, B, C),
and delay is likely numerical (not categorical).
Similarly for your example with servers: X, Y, Z may be levels of a nominal variable and there may
be another variable that measures performance. The performance variable
may be ordinal (perhaps with levels Excellent, Good, Fair, Poor) or numerical (perhaps, orders taken per hour).
In general: Political affiliation, Race, and Religion are good examples of
nominal variables. Examples of ordinal variables are ones with levels
(Strongly agree, Agree, Neutral, Disagree, Strongly Disagree), course grades
with levels (A, B, C, D, F), and so on. For ordinal variables there is a
clear ordering.
Note: Controversy arises when people try to treat levels of an ordinal variable as
numerical. Perhaps it begins with convenience in recording: It is easier to
record 5 for 'Strongly agree', 4 for 'agree', in a spread sheet. Many statisticians agree it is seldom
valid to take numerical means of such 'numbers as labels'. It is more often to valid to speak of the 'median' category (roughly, list all SA first, A next, N next, etc.;
then pick the opinion of the middle opinion in the list).
