Teacher is not an abbreviation, so it has no official full form. It is an ordinary English word for a person who helps others learn, from the verb 'to teach'. The playful expansions you see on social media — such as Talented, Educated, Adorable, Charming, Helpful, Efficient, Responsible — are affectionate backronyms made up after the fact, not a real abbreviation. If a tidy answer is wanted, the honest one is that there isn't one.
In Indian schools
Staff — teachers included — are still records a school keeps: who is on the rolls, which batches they are linked to, and what access they have in the system. RaivatEdu models staff as an entity with role-based access, so each person sees only what their job needs.