What are the practical differences in the practice of Islam between the Sufi practitioners Versus the Sunni and Shiite?
Sunni and Shi'ite is one categorization of Muslims - but Sufism is not another category within that scheme of categorization. For example, there are Sufis among both Sunnis and Shi'ites.
Sufism is characterized by a focus on personal worship and purification. What sets Sufis apart from the general body of Muslims is the body of beliefs and methods employed to achieve those goals. When the methods of worship and purification are derived from the methods of the Prophet (saws) then it is considered to be part of Islam. When those methods are innovated or have no basis in the sunnah, it is considered to be an innovation within Islam and to be avoided. When it involves beliefs that go against the core mainstream beliefs of Islam, it is considered to be kufr and outside Islam.
Here is a short video by Prof. Jonathan Brown of Georgetown University explaining Sufism: http://www.youtube.com/watch?v=5diBm_CG8J0
Messenger of Allah (pbuh) said, "The deeds are considered by the intentions, and a person will get the reward according to his intention
Everything has a zahiri (seen) and batini (unseen) side to it. For example, in salat doing ruku, sucud, reciting Qur'an is zahiri side, and your niyyah (intention) is batini side. If you don't meet both zahiri requirements and batini requirements, your salat is no good.
Correcting the acts of zahir is known as fiqh and sharia, and correcting the act of hidden, the batin, is known as tasawwuf and sufism. That is the tariqa. (Dr.Tahir-ul-Qadri)
Prophet (pbuh) taught us zahiri and batini side of Islam. After prophets time, because no one is perfect, different people specialized with different side of Islam. For example, Imam Abu Hanifah focused on science of fiqh, Imam Bukhari focused on science of Hadith etc...
Allah says (2:151 - Sahih International)
Just as We have sent among you a messenger from yourselves reciting to you Our verses and purifying you and teaching you the Book and wisdom and teaching you that which you did not know.
Allah sent us these things, and some people specialized on reciting Qur'an and become hafiz and qari, some people specialized on purification and became sufi, and some people specialized on Book and became Islamic scholar.
Studying the life of the Prophet , the scholars who propagated the science of tasawwuf understood that a requisite for approaching Allah was abandonment of the common pursuits of the world. They often wore wool because of its simplicity and low cost. In Arabic the word for wool is suf and thus, those who wore it became known as the Sufis.
Sufist generally find it necessary to leave wordly pursuit. They spend most of their time by remembrance of God (dhikr), contemplation (fikr), meditation (muraqiba), and self-examination (muhasiba).
A Sufi is free from any sort of identification because a person can be truly called a "Sufi" after killing the Ego. Yes, during the path of becoming a Sufi, a person may follow a certain school of thought, but this school of thought too has to go in order to be free from any sort of concept which is mandatory in order to be identified as a Sufi.