I think what we are talking about are theories of atonement. How exactly did Jesus "forgive" our debt?
There are usually six theories of atonement listed. I remember them discussed in Brian McLaren's The Story We Find Ourselves In, which I would highly recommend.
Here is a link excerpt of that story talking about atonement. I don't have to time right this minute to do much more. Maybe I could write a post about each theory.
Here are some other links. I haven't look these over very well. They may be misleading or wrong.