So damage causes loss of life but is loss of life necessarily damage?
You are correct. I know it is weird, but it is as you say:
Damage counts as loss of life, but loss of life does not count as damage. This can be shown when redirecing damage to a plainswalker. You can redirect {Lightning Bolt}, but not {Sign in Blood}.
RESOLVED
No things like extort don't cause damage. There are others but that was the first thing that came to mind.
Yeah that is a good example. Never let someone redirect their extort life loss to your pw! ;)