They mean roughly the same. "Fine" also means that you are agreeing but not really agreeing.
In the following situations, I think "fine" sounds better ... but I'm not a native English speaker, so I'm not very sure:
I ended up staying at home, which was fine for me.
And now that he'd accomplished that feat, everything would be fine.
I have to leave now, but I'm sure you'll be fine.
Is "fine" better in these examples? Why or why not?