When it comes to the age of different students in TEFL, there are no set definitions which all teachers agree on.
However, generally speaking, we can talk about the following general Student Age Groups in TEFL:
Young Learners
These are students aged from just a few years old to about 16 or so. In other words, these are students who are probably still at state school as well.
Some teachers, however, talk about Young Learners aged up to about 12. They include another group:
Teenage Learners
Is this a sub-group of Young Learners or a group on their own after Young Learners and before Adult Learners?
The answer to that really depends on who you talk to!
Adult Learners
As the name implies, this is used for students who are over 16 or so, working rather than at school. However, we’re more likely to call EAP students at university “adult” than anything else.
Useful Links
Teaching English to Young Learners – or TEYL: the specialized discipline of how to teach young learners; here generally aged up to about 12 or so
Teaching English to Teenagers – more on how to deal with teenagers and TEFL
Teaching English to Adults – more on the specific problems in teaching English to adults