I have posted this before.
Laotians are Thai people, who speak the same language and dialect as the North Eastern provinces of Thailand. The difference between Laos and Thailand was that the French colonised the Laotian part of Siam in 1893.
After Germany invaded France in 1940 Siam (Thailand) invaded Laos to claim the country back. It is a bit (but not exactly) like having people on either side of the Waikato River forming different countries, even though they speak the same language and share the same history.
To put it in another perspective the Thai people originate from Yunan, Xuangxi and Xangzhou in southern China. Over the centuries they emigrated into the hill country and valleys of North Vietnam, Laos, Siam and Myanmar.
Also the Kingdoms of the Isan (Korat) Plateau which Thailand and Laos share, and through which the Mekong flows down to Vietnam and Cambodia were in the past ruled by the Angkor Wat (Cambodian) empire.
What that basically means is there is no significant difference between Lao and Thai people. Thailand is actually a new name for Siam invented after WWII, which is another story.
Different countries. Same genetic makeup potentially. It's still incorrect to say half-Thai.
I think the Lao people are Tai, not Thai. (Thai are also Tai).