Bonjour Clare,
You are right that context helps although the lesson explains the difference quite clearly. Here are some examples:
Ancient / old : noun + ancien(ne) OR After noun= Ancient
C’est une voiture ancienne = it is an old car
C’est un appartement ancien = it is an ancient/old building
Former / previous : ancien(ne) + noun OR beFore noun = Former
C’est mon ancienne voiture = it is my previous car
C’est mon ancien appartement = it is my previous flat
I hope this is helpful.
Bonne journée!