Is multi-class classification the same with categorical classification?
Yeah, the answer is as simple as :


Binary Classification means only 2 targets to find.
Multilabel / Multiclass / Multinomial Classification means more than 2 targets to find.


In Supervised Learning, you will have : 


Classification (class of 0, 1 etc..)
Regression (continuous values 84.2, 105.8 etc..)


Categorical and class means the same and are the opposite of Regression which are continuous variables 

You can find example on https://scikit-learn.org/stable/supervised_learning.html#supervised-learning