Depression can be explained in terms of faulty and irrational thought processes and perceptions. The behavioural approach focuses on maladaptive behaviours whilst the cognitive approach focuses on the thoughts that underpin the behaviour.
Ellis's ABC model

Depressive mistakenly blame external events for their unhappiness. It is their interpretation of these events that is to blame for distress.
Ellis's ABC model: A
A is for the Activating Agent: irrational thoughts are triggered by external events.
Ellis's ABC model: B
B is for Irrational Beliefs: This includes utopianism (life should always be fair), mustabation (I must be like, I must do well) and catastrophising (it is a ditaster when things don't go well).
Ellis's ABC model: C
C is for Consequence: triggered by the belief
Beck's Cognitive Triad

Negative thoughts and cognitive vulnerability are automatic. Negative schemas trigger depressive thoughts. Schemas are developed in childhood and continue to adulthood- negative schemas lead to a negative viewpoint of life.
The cognitive triad is made up of cognitive bias and negative schemas.
Negative schemas include: ineptness schemas (make the depressive expect to fail), self-blame schemas (make the depressive feel responsible for all misfortunes) and negative self-evaluation schemas (constantly remind the depressive of their worthlessness).
Cognitive bias includes: arbitrary inferences, selective thinking, overgeneralisation, catastrophising, personalising and black and white thinking.
The cognitive triad says that negative views about the world, cause negative views about the future, which cause negative views about yourself.