Redirected damage retains its information. For example, your opponent attacks you with Slith Firewalker (which reads, in part, “Whenever Slith Firewalker deals combat damage to a player, put a +1/+1 counter on it.”) and you block with a creature enchanted with Ward of Piety. If you activate Ward of Piety, targeting your opponent, the Slith’s ability triggers during the combat damage step and it gets a +1/+1 counter. It’s still combat damage.