Empathy vs. Sympathy

I came across this short video recently, which is taken from a talk about 'The Power of Vulnerability,' and it has stuck with me for days.  As someone who struggles with depression and anxiety, which used to be crippling and thankfully is not any longer, it is a relief to have the very real difference between sympathy and empathy explained so succinctly.
When we're having a bad day, don't we just want someone to say, 'I'm sorry you're going through this.  You're not alone- I've had bad days, too'?
Sometimes, when I'm having a rough time and someone tells me what I could be doing to feel differently or better, it makes me feel like I'm unhappy because I'm doing something wrong, i.e. I am responsible for my unhappiness.  When things don't go our way, it's okay to feel bummed about it or upset that it didn't go the way we think.  (When these emotions don't go away, it's time to seek help.)  The trick is finding those people who will come into our deep, dark holes with us, give a hug, allow us to be vulnerable for a while, then help us be strong.
I'm so glad to have people in my life who do this for me.  I hope you do, too.