You can also say "I feel numb", for depression - It is similar to "nothing". Some say "I feel nothing", after a break up when heartache is overwhelming.

In this context, they mean basically the same thing, yes. You can use both when talking about depression or apathy.

So you mean they are different..?

to "feel nothing" implies a numbness to pain or inability to feel - think of pain medication, which blocks feeling or sensation. to "feel empty" implies you are lacking feeling or lacking something. Think of an empty cup in which you might want coffee or water to be poured into it.

Thank you so much!