The difference between Trading and Gifting lies in the expectations of a fair exchange. If you clicked the wrong link and meant to investigate more into the Trading trophy, refer to this:
The Trading Up trophy in .hack//G.U. Last Recode worth 18 pointsConduct a trade with an ally. (Allies will still count as allies before exchanging member addresses.)To gift an item to an ally, either meet with them in the root town, such as Mac Anu, or go near the Chaos Gate and add them to your party. Talk to them and you will see:
Talk
Trade
Gift
Cancel
Gift is the selection you wish to make. Choose the item you wish to give and they will say a response for accepting the gift. If it is an item that they can use right away, they will appreciate it and actually equip it, which is ideal for gearing your party members with better equipment. However, this doesn't require anything in particular other than giving a gift to them.