A polite offer meaning "Shall I...?" — used to offer to do something for someone.
荷物を持ちましょうか？
Shall I carry your luggage?
窓、閉めましょうか？
Shall I close the window?
明日の準備、手伝いましょうか？
Shall I help you prepare for tomorrow?
A suggestion meaning "Shall we...?" — used to propose doing something together or to invite action.
映画に行きましょうか？
Shall we go to a movie?
そろそろ出かけましょうか？
Shall we head out soon?
今日はこれで終わりにしましょうか？
Shall we finish for today?