Unite - if different people or organizations unite, or if something unites them, they join together in order to achieve something (come or bring together for a common purpose or action):
-Our goal is to unite the opposition parties and defeat the President.
(unite against/behind)
- Party members united behind their leader.
(unite to do something)
- In 1960, the regions united to form the Somali Republic.
Unify - if you unify two or more parts or things, or if they unify, they are combined to make a single unit (make or become united, uniform, or whole):
- Strong support for the war has unified the nation.
- His music unifies traditional and modern themes.
(Longman, Oxford Dictionaries)