Podría ser un problema relacionado con la conversión de la entrada, intente usar str_to_date y literal Where (use una conversión de formato de fecha adecuada basada en su formato, mi ejemplo es "%d-%m-%Y")
$modelStockDetails=StockDetails::find()
->where(' date(created) between STR_TO_DATE("'. $start_date . '", "%d-%m-%Y" )
AND STR_TO_DATE("' . $end_date . '", "%d-%m-%Y" )' )
->andwhere(['receiving_order_id' =>$modelRecevingOrder->id,'deleted' => 'N'])->all();
o para evitar el uso de var en sql, podría usar
$modelStockDetails=StockDetails::find()
->where(' date(created) between STR_TO_DATE(:start_date, "%d-%m-%Y" )
AND STR_TO_DATE( :end_date, "%d-%m-%Y" )', [':start_date' => $start_date, ':end_date' => $end_date] )
->andwhere(['receiving_order_id' =>$modelRecevingOrder->id,'deleted' => 'N'])->all();