Which of the following would be classified as categorical data? age, gender, height, letter grade on most recent exam, percentage correct on most recent exam, number of likes to a Facebook posting, weight, eye color, gas mileage of your car
Categorical data have values that cannot be ordered in any obvious, compelling way.
Gender is an example. Male is not less or more than Female.
Eye colour is the other one in your list.
Letter grades are class data: there is a compelling order in them: you have to order them from high to low (or low to high).
The other examples you mention are more or less continuous data: there are many possible values, that you may group into classes, but you have a certain choice about class width.