The root of the term "typologies" is "types", with the connotation of a qualitative difference among them.  A typology is thus a categorical variable but not an ordinal variable.  If there were an underlying ordinal variable to these types, we would not find it necesssary to regard them as qualitatively different.

Sometimes typologies are generated by "crossing" two ordinal variables.  This can be valuable, but only if the resulting typology tells us substantially more than the sum of the information from the two variables.  In other words, there has to be an interaction between the two variables.

A concrete example will help, and Babbie mentions a good one:  a typology of "pro-life" attitudes based on crossing attitudes about abortion with attitudes about capital punishment, as in the following table:

The key issue is whether the people in the various cells differ from each other in ways that could not be understood by the individual factors (capital punishment;  abortion) taken alone.  For example, the Catholic Church's official doctrine would be placed in cell A:  it opposes both abortion and capital punishment.  But many anti-abortion activists fall in cell C:  they oppose abortion but see nothing wrong with capital punishment.  These two groups seem to differ in more profound ways than their mere attitudes about capital punishment.

Or compare cells B and C.  Are they both pretty much equal in their regard for life, protecting it in one area but not in another?  Or are they pretty much equal in that they are both confused, valuing life in one area but not in another?  No, they are quite different from one another!  For one thing, they tend to vote for different political parties.

In short, A-B-C-D is a typology.  Each group has its own identity that goes beyond their mere policy positions on the questions of abortion and capital punishment.