The ethnic Lao (amongst themselves they call each other "Tai") are found in Northern Thailand (former Lao kingdom referring themselves as "Tai Yuan"), Northeast Thailand (Cent…ral Thais a.k.a. Siamese people call them "Isan" but locally they still call themselves Lao), Yunnan China (Tai Lue), Northern Vietnam (Tai Dam), and the Shan state of Burma (Tai Yai)..
The name "Laotian" came about when the French took interest in colonizing Indo-China (Vietnam, Laos, and Cambodia). Realizing the ethnic Lao was one of the leading ethnic groups in the region, they often confused the different Lao Muangs or Kingdoms as one or the same. The ethnic Lao in Myanmar (Burma) are referred as "Shan" by the Burmese, so the term stuck on the French to call the Lao people (especially the Lao group from the LanXang kingdom known as Laos today), Lao+Shan or simply spelled by the French "Laotian" (pronounced as Lao Shan). ( Full Answer )