To expand the answer before:
Every party member gets his own item drop that can be seen on the floor only by that person until it is picked up. That said, it means you can get a set item, but your team members can get nothing. For example if you trigger the shelf in Halls of Agony, you may or may not have the drop from it, and it can be normal, magic, rare, legendary or legendary set.
If there are 4 of you in a party, there could be a (very rare) occasion when the same shelf drops nothing for you, rare for one of your friends, legendary for another and the fourth gets legendary set. All the variations are possible.
Each legendary drop can be shared with another party member for 2 hours from the time it dropped on you. That means, if you get a drop that doesn't give you any boost, but boosts your friend in the party, you can give the item to him/her by dropping it on the floor again from your inventory.
This only works if the person was in the game when the item dropped.
TL;DR: The legendary and set items can be traded inside the same party for two hours after drop. Direct drop (the drop that was not picked up yet) that you see on your screen cannot be seen by anybody else in the party unless you pick it up and drop it again.