If the relationship has a different primary address listed on the record before processing the form:  
When the Same Address as checkbox is marked, the individual primary address will overwrite with the applicant/student address that was listed on the form. The original primary address information listed on the individual record will no longer show on the Bio 1 or Addresses tab of the record.

If a different individual address is entered on the form AND the Same Address As checkbox is marked: 
If the individual enters a different address on the form than the student address listed, and the Same Address checkbox is marked, the student address will still be written to individual record. The address entered in by individual is lost. 
Note: It is best practice when using the Same Address is checkbox, to hide address fields when the Same Address As checkbox has been marked.