The only real difference was the succession of leadership, to who must it go. The Sunni believe that it went to the correct people, whilst the Shia said it should've been the Prophet Muhammad's (peace and blessings of God be upon him) cousin, Ali.
This is where the initial difference stems, later they developed other beliefs/theology and separated into different sects. It must be noted that the Shia did start off as a political group at first then changed from there.