I was recently asked whether the word Ajaan can be used for people who are not ordained, and rather than limit the answer to one person, I thought I would share it with all of you who might be interested in the subject.
The word Ajaan, or actually "Aajaan" (อาจารย์) as the Thais pronounce it, comes from the Pali word "ācariya" which comes from the verbal root "car" with the prefix "ā". The various meanings, according to the Buddhist texts, could be:
sissānaṃ hitam ācaratīti = one who acts for the profit of one's students
ādito cāreti sikkhāpetīti = one who causes one's students to behave and train from the beginning
ādarena caritabbo upaṭṭhātabboti = one towards whom students should behave well and care for with affection.
ā bhuso sissānaṃ hitasukhaṃ caratīti = one who acts for the great benefit and happiness of one's students
abhimukhaṃ katvā caritabboti = one towards whom students should behave in such a way as to set in front (ie one whom they should follow).
āpāṇakoṭikaṃ katvā caritabbo upaṭṭhātabboti = one towards whom students should behave well and take care of for their whole lives.
(From ศัพท์วิเคราะห์, พระธรรมกิตติวงศ์)
In brief, ācariya means "teacher", and so anyone can be called ācariya if they teach. In Thailand, the word aajaan is used for anyone who is a teaching position, whether they teach worldly subjects or Buddhism, and whether they are ordained or not.