Ask your T what s/he meant. All these definitions are always so personal, and all any of us can do is guess what your T might have meant.

For me, the concepts are pretty much the same. Living is no more or less than existing. It is possible to enjoy existence - life - or not, but for me the two terms in themselves have no connotation of more or less enjoyment.

Depression is a very wide umbrella term, and it's not possible to say that somebody who does or feels x is depressed or not. It depends on a lot of different things.