What is the difference between categorical (qualitative) data and numerical (quantitative) data?

Hint: Let us start with the basic definition of categorical data, it is also called qualitative data while numerical data is called quantitative data. This is because categorical data is used to qualify information before classifying data according to their similarities.

Complete step by step solution:
Categorical data: -
Categorical data represents named qualities of an observed phenomenon. It includes the usage of words to describe the names or properties of objects, like their color, shape, and texture. For example, we can say that “The color of an apple is red” is something which describes the quality of the color of the apple. In data science, we refer to categorical data as “qualitative data”. We do so as they describe the quality of the thing that they represent. However, most beginners more intuitively understand the term “categorical” rather than “qualitative” so it is recommended that we conceptualize this type of data as “categorical” data.
Some of the examples are scents, beauty, flavors, etc.
Numerical data: -
Numerical data represents measured quantities of an observed phenomenon. It includes the usage of numbers to describe the measurement of objects like their size, weight and velocity.
In data science, we refer to numerical data as “quantitative data”. We do so since they describe the quantity of the thing they represent.
Some of the examples are collected data that can just be observed and evaluated.

Note: When answering this question, there is a chance that most students might get confused between the terms “quantitative” and “qualitative”. So it is recommended that students should refer to “numerical” data as “quantitative”. Note that measure difference between these two is that qualitative data are unstructured and determines depth of understanding while the other one is structured and determines level of occurrence.