The difference between constructing and drawing geometric figures is as follows:
To construct geometric figure you use many tools like protractor, compass, ruler, scale, square, among others. So you need an accurate representation of the geometric figure. On the other hand, to draw a geometric figure you only need a pencil to do that. You don't need an accurate representation of the geometric figure.
A real-world example of each:
Think about an civil engineer who is constructing a building. He would need many tools to do that. In fact, he would need an building which is an accurate representation of the drawings he made using a software. He would need the accurate measurements and the correct location of each characteristic points of the building. So, this is the construction. On the other hand, when starting with the project, the civil engineer maybe took a paper and began drawing an sketch of his building, he only needed a pencil to do that, so this is the drawing made by hand.
