Muslims never identify themselves or ask if they are Sunni or Shiaa because they are both Muslims *.  They both follow the same Qur'an, believe in the same One God, and believe Mohammed is his final and last messenger.  They both pray, fast, give Zakaht, and perform Pilgrimage.  They both pray at the same Mosques, and eat the same food and marry each other. 

Muslims belong to one of the two main branches of allegiance in Islam -- the majority are Sunni  (comprising more than 90% of believers) or Shiaa. The basic difference between the two is that the Shiaa School believes in the necessity for a spiritual leader from the Family of the Prophet Muhammad, hence a religious structure. The Sunni School on the other hand, does not necessarily require the same.

* History shows foreign occupation always use the strategy of "Divide and Concur", in order to weaken their enemies, reduce their casualties, and provide for a long-term presence on the occupied regions. 

Each local Muslim Community, whether Sunni or Shiaa, has one or more religious leaders (people who have attained formal Islamic education or who are proficient in Islamic knowledge). This kind of leader is often referred to as an Imam, Director of the Islamic Centre, or Khateeb (one who gives the Sermon, or Khutba).