A Muslim is one who believes in one God and strives for total reorganization of his life according to God’s revealed guidance “holy Quran” and the sayings of the Prophet Muhammad. He also works for building human society on the same basis. 
 
 islam was completed during the life time of prophet  
 
Allah said in quran  
 
5:3;This day, I have perfected your religion for you, completed My Favour upon you, and have chosen for you Islam as your religion.Al Quran 
 
what happened after prophet death is political not relegion problem  
 
there is nothing like shia in quran or hadeeth  
 
its only islam and muslim  
 
Allah said in quran  
 
41:33. And who is better in speech than he who [says: "My Lord is Allah (believes in His Oneness)," and then stands straight (acts upon His Order), and] invites (men) to Allah's (Islamic Monotheism), and does righteous deeds, and says: "I am one of the Muslims."  
 
its forbidden in islam to make any sect  
 
Indeed, those who have divided their religion and become sects - you, [O Muhammad], are not [associated] with them in anything. Their affair is only [left] to Allah; then He will inform them about what they used to do. [6:159]

The word Sunni comes from the Arabic word , Sunnah, which means : the way of prophet Muhammad (Allah's peace and blessings be upon him, his family and companions). so Sunni means : the one who follows the way of prophet Muhamad according to Quran and the authentic traditions of prophet Muhammad. 
 
Shia sect started after the death of prophet Muhammad due to differences of opinion of some people who should be successor Caliphate.  
 
Shia means who try to support the Ali as the caliphate 
 
the word Shia comes from the Arabic word,  shaya: which means to support the family of prophet Muhammad. this sect appeared to Support 4th caliph , Ali Ibn Abi Talib,who was cousin of prophet Muhammad. so at the time of prophet Muhammad , there was no shia. shia appeared later , and later they went far from Islam. 
 
 
 
Sunni means : the one who follows the way of prophet Muhamad according to Quran and the authentic traditions of prophet Muhammad. which is exactly quran says and the prophet said and all his companions followed it including Ali ra. 
 
by the way , the main stream Muslims are Sunni (about more than 90% of Muslims are Sunni), while shia are less than 10 %.