How to describe the relationship? For me, I hold that C.S. Lewis had the best description, in Mere Christianity:
"...handing everything over to Christ does not, of course, mean that you stop trying. To trust Him means, of course, trying to do all that He says. There would be no sense in saying you trusted a person if you would not take his advice. Thus if you have really handed yourself over to Him, it must follow that you are trying to obey Him. But trying in a new way, a less worried way. Not doing these things in order to be saved, but because He has begun to save you already." (emphasis mine)
I think this very well sums up what I have experienced in my life. As soon as I accepted that Jesus really, truly did love me for who I am--warts and all--this did not lead to hedonism or the misuse of His grace. Far from it! Rather, I ended up doing more good works than before, and yet worrying less about it: I became more committed to following Him, and less fearful of whether my following was good enough.