Array

=======================================
foreach ($period_a as $key => $value) {
    $result['data'][] = $period_a[$key];
    if ($period_b_start_date && $period_b_end_date) {
        $result['data'][] = $period_b[$key];
        if ($period_a[$key]['payment_type_id'] == $period_b[$key]['payment_type_id']) {
            $result['data'][$key]['sum_b'] = $period_b[$key]['sum'];
            $result['data'][$key]['total_b'] = $period_b[$key]['total'];
        }
    }
}
header('Content-Type: application/json');
echo json_encode($result);

=============== PERIOD A ===============
{
  "data": [
    {
      "payment_type_id": 2,
      "description": "Χρεωστική Κάρτα",
      "sum": "12.50",
      "total": "12.50"
    }
  ]
}

=============== PERIOD B ===============
{
  "data": [
    {
      "payment_type_id": 1,
      "description": "Μετρητά",
      "sum": "20.83",
      "total": "27.08"
    },
    {
      "payment_type_id": 2,
      "description": "Χρεωστική Κάρτα",
      "sum": "6.25",
      "total": "27.08"
    }
  ]
}

=============== TARGET ===============
{
  "data": [
    {
      "payment_type_id": 1,
      "description": "Μετρητά",
      "sum": "20.83",
      "total": "27.08"
    },
    {
      "payment_type_id": 2,
      "description": "Χρεωστική Κάρτα",
      "sum": "12.50",
      "total": "12.50"
      "sum_b": "6.25",
      "total_b": "27.08"
    }
  ]
}