Stress is when you feel that the demands placed on you are too great, when you feel that you cannot cope.
Signs of Stress:

Overwhelmed
Why is everything so hard?
Difficulty in sleeping
Inability to concentrate
Feeling as if life is spinning around you

Depression is when you experience sadness or hopelessness for most of the day for over 2 weeks.
The symptoms and behaviours associated with this disrupt your ability to live your normal daily life.
Signs of depression:

Discomfort in the body
Feel empty, helpless, or worthless
Lose interest in activities that once were pleasurable
Experience loss of appetite or overeating
Have problems concentrating, remembering details, or making decisions
May contemplate or attempt suicide
Experience insomnia, or excessive sleeping