Tai are people of mainland Southeast Asia, including: The Thai or Siamese (in central and southern Thailand), The Lao (in Laos and northern Thailand).
Some historians claim that Tai people are, in BC 3000, the inhabitants of Asia, central part of the land now known as China. 
Rev. William C. Dodd, a Christian missionary, stated that the Tai settled in the land now known as China before Chinese arrived, based on Chinese annals of 2200 BC. 
According to Chinese annals, the ‘Ta Muong’ or ‘Great Muong’ lived in the northwestern part of Szechwan province, in western central China, even before Chinese migrated from the west. Ta Muong would have been the ancestors of the ‘Ai Lao’ or ‘Tai’ race known as Pa, Pa Lao or Pa-Yi in China who later founded the powerful ‘Nan Chao Kingdom’ in Yunnan province. In BC 1558 the Tai had spread over a vast territory nearly across the whole width of modern China. Tai have never been called ‘Chinese’, nor claimed to have any ethnic links with the Chinese race. Throughout Chinese historical records the Chinese name for the ‘Tai’ has constantly been changed.
According to American Missionary Rev. W.W. Cochrane ‘Tai’ means ‘Free’. Sometime it is also written as ‘Dai’ when refer to Tai in China. The Dai ethnic group in China, with a population of about 1.2 million, mainly lives in ‘Dehong Dai-Jingpo Autonomous Region’ and ‘Xishuangbanna’ (as written as ‘SipSongPanNa’, which means twelve productive rice fields) Autonomous Prefecture in the southern part of Yunnan province. The main Dai groups in China are Dai Lu, Dai Nua and Dai Mao.
According to Travel China Guide, Dai is the name of the nationality, which means ‘freedom’ or ‘human beings’.
‘Tai’ or ‘Shan’ is now used as a generic word to cover the whole race spelled by French as ‘Thay’. The name is said to mean ‘The Free,’ or ‘ Free Men.’ 
The name ‘Shan’ refer to Tai in Burma @ Myanmar.
Shan population in Burma is about 5 million (10% of Burma total population)
Why do they call themselves ‘Tai’ or ‘Free’ or ‘Freedom’ or ‘Freemen’? Most likely, according to the history of Tai people, they were under attack many times by many groups like Monkhmer, Mongol, Chinese and Burmese for centuries. Their Kingdoms had been destroyed Kingdom by Kingdom. They were dispersed to many places in Southeast Asia because of war. They ended up ‘people without country’ in other countries in such as China, Burma, India and Vietnam and become a minority group of people in those countries. They would long for freedom.
The great Tai race, who number today about 100 million, had established numerous Kingdoms and States in the past and still govern the two nations of Thailand and Laos. Tai people consider Thailand and Laos as Tai countries existing today. 
Click here to read more about Tai/Shan people in pdf format
Other source http://www.shanland.org/resources/history/