Responsibilities and concerns are not the same thing. Responsibilities are things that I can control. Concerns are things I cannot control.
Defining responsibilities and concerns can get tricky because what may seem like a responsibility might actually be a concern.
For example, I have a responsibility to be punctual at work and to complete my tasks. (Those are things within the realm of my control. However, if I have a co-worker who gets annoyed at how slow I complete my tasks (that won’t contribute to missing deadlines), that may be a concern. (My co-worker’s reaction is out of my control; it is only a concern if I care about their reaction. If not, then it is not a concern.)
There are trickier things to define. Is a spouse’s emotional well-being a concern or a responsibility? If an adult child has a terminal illness and refuses treatment, is abiding by his or her decision a concern or a responsibility?
A marked Christian way of looking at this would be that when there are responsibilities, a Christian must obey any duties he or she has been given; when there are concerns, a Christian must trust that God will handle anything he or she is faced with. Hence, responsibilities are within our control and concerns are out of our control.
Delineating responsibilities and concerns lightens the load of depression and anxiety a bit. Knowing that I am not responsible for everything eases my burdens — and alleviates many of my concerns.