You are correct: categorization applies a label (or 'class') to any given data point. As you mentioned, this term is category. Consider malware classification: given a file, is it malware or not? (The "label" will be the 'yes' or 'no' answer to this question.)
The purpose of regression, on the other hand, is to forecast an actual value (i.e. not categorical). Predicting someone's weight based on their height and age is an example.
So, in either of the questions you've posed, the answer boils down to what you're looking for from your prediction: a category or a true value?
Regression is the process of finding the relationship and the effect of this relationship on the outcome of the future value of an object, whereas classification is the process of grouping data into categories for the most effective and efficient usage. 2.In order to predict numerical and categorical data, classification is employed, whereas regression is used to forecast numerical data.