Both are used - the language itself can be called Lao or Laotian. Lao is better to use though, due to historical reasons. Lao is more polite to the locals (general English speakers use them interchangeably). Michelle https://www.italki.com/michelle

If you are from Laos you are Lao in the Lao language but in other languages like English they say Laotian.

Laotian, I've never seen Lao in use.