hmmm let me see if I can clear that up.

Living to work implies that the purpose of your living is to go to work.

Working to live means the purpose of your working is to be able to have a living. I do not think I live to work. My life has many other purposes than just going to and from work every day, running the rat race and getting that promotion.

But by contrast, I do work to live. If I didn't need the income, if I could live comfortably without it, I probably wouldn't be working.