荷造り and 包装: preparing luggage and wrapping an item
Compare packing for a move with wrapping an object. Wrapping can be part of packing without establishing completion of the entire packing task.
Packing for movement
荷造り, read にづくり, means packing. 引っ越し前夜まで荷造りが終わらなかった。 says that packing had not finished by the night before the move.
Read the scope of packing for the move. Wrapping one object does not by itself establish completion of all packing.
Wrap one object
包装, read ほうそう, means wrapping or packaging. 贈り物を青い紙で包装した。 says that the gift was wrapped in blue paper.
Wrapping the gift is a completed action. It does not establish that packing for a move has been completed.
Wrapping within the packing task
割れ物を新聞紙で包みながら荷造りした。 says that someone packed while wrapping fragile items in newspaper. The actions take place together.
Wrapping can be part of packing. Read the relation between one wrapping action and the broader packing task without requiring separate events.
Does 包装した。 for a gift alone establish that all 荷造り for a move has finished?
Show the answer and why
No. It concerns wrapping that gift. Completion of the entire moving-luggage preparation needs separate information.

