Trigger means, "If x, then y." If the monster is bloodied, then they get an extra attack, or their special attack automatically recharges, or something like that. It's quick, easy to remember, it's interesting and then it's gone.
Bloodied as a condition means that the effects of that condition have to be remembered, considered, and accounted for for the rest of the combat. So when we played 4e, we used to put different colored rings around the minis when they got a condition. The monster minis would get so full of conditions, it could barely be seen for all the condition rings hanging off it, like some miserable condition Christmas tree.