Being stressed-out is the same as burnout. When you are faced with the burdens of stressors, such as relationship problems, financial problems, or work problems, you may have so much stressors that you are not able to cope with them. If you don't find a way to either decrease the stressors or to cope with them adequately, then prolonged exposure to the stressors can start to wear on you and break you down, and you may then develop burnout, which is another term for stressed-out.
The symtoms of burnout include irritability, fatigue, insomnia, poor concentration, poor appetite, anxiety, depression, anhedonia, negativity, and social isolation. Burnout or being stressed-out is where you also may meet criteria for an adjustment disorder, which is a mental health problem that precedes anxiety or depression. So if the stressors continue, and you still are not able to cope, then the burnout may develop into a depressive disorder or an anxiety disorder.
So if you do not decrease your stressors or build adequate coping skills when you are stressed-out, then this may development into depression or anxiety.