Personas
The purpose of a persona is to create a realistic and informative profile of a potential user of a product. In these personals there is a variety of demographics, interest, skill levels, and goals that a real user might have that can be analyzed by a company.
Empathy Maps
The purpose of an empathy map is to analyze a users actions from the initial desire for the product to researching competition, to using the product, to selecting the product or going through the cycle again until the user had found the proper product they wish to use.