This video offers a great explanation as well as a demonstration of the two-point and three-point perspectives during sketching.

https://youtu.be/lqsp_GL18yM

There are two ways they can be distinguished.

1. In two-point, lines are either horizontal or recede toward one of the two vanishing points. In a three-point perspective, all lines recede toward one of the three vanishing points.

2. In the three-point perspective, the three vanishing points make up a triangle, with the viewer’s center of vision roughly in the middle.