Dependency theory: 

Dependency theory is an approach to understanding the economic development of a country in terms of the external influences like political, economic, and cultural effects on national development policies.

Modernization theory:

Modernization theory is an approach to understanding how traditional or underdeveloped societies transform to modern societies.

The main difference between these theories is that dependency theory focuses more on poor and underdeveloped countries and modernization theory focuses on rich and developed countries.