An Existential Crisis occurs when you think life is meaningless, lacks direction, purpose and doesn’t hold any value. Many of the day-to-day activities may seem silly or superficial. Hence you tend to become inactive exploring why the world is not changing at all.
On the other hand, depression is a clinical case whereby you tend to withdraw from others exhibiting a variety of symptoms that may have been caused by a mood disorder. It could be caused by a separation in relationship, loss of wealth or business, loss of a dear one, fall in career and so on.
Psychiatrists believe depression is caused by a chemical imbalance in the brain. On the other hand, an existential crisis is more attitude-related than emotional.