Are there some variables where it can be difficult to assess whether they are purely categorical?
For example: To assess the level of pain that a patient is in, you use a scale between 1 and 10.I wouldn't consider pain score to be a categorical variable here, just discrete; this is because it is a measurement (even if it is subjective).
Conversely if I have something such as tumour stage, it is still a discrete variable between say 1 and 4, however I am more tempted to say these are categories. The thing is, increasing value in the Tumour stage does actually have meaning: more likely to have aggressive disease. For categories such as hair colour, or gender, there is no numerical relationship between the categories!
The only thing I can really see is that in discrete variables, each step increase has the same meaning (thus increase of 1-2, 5-6 and 9-10) is the same. Whereas with tumour stage va the step sizes don't mean the same thing : 1-2 is different than 2-3 and 3-4 because the tumour aggression is probably not linear.
This has implications when running logistic regression models, where you could treat categorical variables differently (names you code them differently).