Taking damage and losing life is like going in the rain and getting wet. One causes the other, but the second doesn't directly imply the first. Only things that use the word "damage" count as damage (and, of course, combat damage from attackers/blockers). That causes you to lose life (so taking damage will trigger anything that triggers upon losing life), but there are other ways to lose life. The most common is through effects that specifically say that you lose life, like Blood Tithe. Also, paying life for cards like Wall of Blood. Also, any time your life total is set to a number lower than your current one, it counts as losing life. So if you're on 10 and you control 2 creatures when a Biorythm resolves, you lose 8 life. None of this counts as taking damage.
Edit: The comprehensive rulebook does indeed make a distinction between damage and loss of life. Observe these quotes:
118.3a. Damage dealt to a player causes that player to lose that much life.
...
118.4b. Next, damage that's been dealt is transformed into its results, as modified by replacement effects that interact with those results (such as life loss or counters).
There are several others as well. Remember - Magic is a VERY literal game. Only an effect that uses the word "target" counts as targeting, only an effect that uses the word "draw" counts as drawing, and only an effect that uses the word "damage" counts as damage. The cards say exactly what they mean.
@brockhammy: I believe you're actually thinking of the text "Damage causes loss of life", which is on several cards (for example, Lich's Tomb, Tainted Sigil, and Children of Korlis).