収納 and 片付ける: storing items and tidying a space
Compare storing clothes in a box with tidying a room. Storage may be part of tidying without establishing completion of the whole room.
Put items in a storage space
収納, read しゅうのう, means storage. 季節外れの服を箱に収納した。 says that out-of-season clothes were stored in a box.
箱に identifies the storage location. Storing these clothes and tidying the whole room have different scopes.
Tidy the space with 片付ける
片付ける, read かたづける, means tidy up or put away. 来客の前に、散らかった部屋を片付けた。 says that the messy room was tidied before guests arrived.
The room is the object of the tidying action. Storage can be included in the process, so the two words do not require separate events.
Create a usable storage space
階段の下を収納として使えるように改装した。 says that the area beneath the stairs was remodeled so it could be used for storage. Remodeling is the completed action.
Making a usable storage space does not establish that particular clothes have already been placed there. Read space preparation, item storage, and whole-room tidying separately.
Does 収納した for clothes in a box alone establish that the whole room was 片付けた?
Show the answer and why
No. Storing the clothes can be part of tidying, but completion of the whole room needs a separate statement.