You "drop" classes before the add/drop date (also called the Late Schedule Adjustment deadline) because you can do it yourself in mySDSU. You do NOT need permission to drop classes.

After the add/drop deadline, you are responsible to complete the class schedule you created for yourself. The University allows you to "withdraw" from some or all your courses ONLY if you have experienced something "serious," "compelling," and "beyond your control," with official documentation from a "third party." The University determines if you will be allowed to withdraw (compared to "drop," which you decide for yourself). 

Here is the link to the webpage with instructions and how to access the form. Don't fill out the form without first reading the instructions.