Depression
Clinical depression ("major depressive disorder") is more than just feeling sad, discouraged, or burnt out. It is a medical condition that has both genetic and environmental causes, and leads to significant distress and reduced ability to function in many areas of life including self care, relationships, and work/study.
Common symptoms along with a depressed mood include fatigue, reduced motivation, a lack of enjoyment ("anhedonia"), poor or increased appetite, weight loss or weight gain, and negative thoughts (e.g. hopelessness, excessive guilt, or self harm/suicide).
Clinical depression can accompany other conditions such as trauma or anxiety.
Bipolar disorder
Bipolar disorder is a condition that is characterised by unstable mood states that oscillate between high ("mania/hypomania") and low (depression). These phases can be interspersed with periods where mood is level ("euthymic").
Bipolar disorder, when severe, is classed as "Type 1" when it is associated with behaviour that requires emergency care or hospitalisation, or psychosis (delusions, hallucinations). It is classed as "Type 2" when episodes are not associated with the above, but can nonetheless be very debilitating as episodes can be more frequent ("rapid cycling"), destabilising, continue to affect one's ability to function across all domains of life, and depressive episodes may be associated with a high risk of self harm or suicide.
Bipolar disorder might be mistaken for non-bipolar depression, only coming to light when traditional treatments for depression fail or worsen the condition. It is often concurrent with other conditions such as ADHD, anxiety, and trauma.