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It is the classical L2 distance for floating point descriptor and HAMMING like distance for binary descriptor.

You can check it with the following code:

  cv::Mat img1 = cv::imread("opencv-3.1.0/samples/data/aero1.jpg");
  cv::Mat img2 = cv::imread("opencv-3.1.0/samples/data/aero3.jpg");

  cv::Ptr<cv::Feature2D> sift = cv::xfeatures2d::SIFT::create();
  std::vector<cv::KeyPoint> trainKeypoints;
  cv::Mat trainDescriptors;
  sift->detectAndCompute(img1, cv::Mat(), trainKeypoints, trainDescriptors);

  std::vector<cv::KeyPoint> queryKeypoints;
  cv::Mat queryDescriptors;
  sift->detectAndCompute(img2, cv::Mat(), queryKeypoints, queryDescriptors);

  cv::Ptr<cv::DescriptorMatcher> matcher = cv::DescriptorMatcher::create("BruteForce");
  std::vector<cv::DMatch> matches;
  matcher->match(queryDescriptors, trainDescriptors, matches);
  std::cout << "matches[0]: trainIdx=" << matches[0].trainIdx << " ; queryIdx="
      << matches[0].queryIdx << " ; dist=" << matches[0].distance << std::endl;

  double my_dist = 0.0;
  for(int j = 0; j < trainDescriptors.cols; j++) {
    my_dist += (trainDescriptors.at<float>(matches[0].trainIdx, j) - queryDescriptors.at<float>(matches[0].queryIdx, j))
        * (trainDescriptors.at<float>(matches[0].trainIdx, j) - queryDescriptors.at<float>(matches[0].queryIdx, j));
  }
  std::cout << "my_dist=" << cv::sqrt(my_dist) << std::endl;

It is the classical L2 distance for floating point descriptor and HAMMING like distance for binary descriptor.

You can check it with the following code:

  cv::Mat img1 = cv::imread("opencv-3.1.0/samples/data/aero1.jpg");
  cv::Mat img2 = cv::imread("opencv-3.1.0/samples/data/aero3.jpg");

  cv::Ptr<cv::Feature2D> sift = cv::xfeatures2d::SIFT::create();
  std::vector<cv::KeyPoint> trainKeypoints;
  cv::Mat trainDescriptors;
  sift->detectAndCompute(img1, cv::Mat(), trainKeypoints, trainDescriptors);

  std::vector<cv::KeyPoint> queryKeypoints;
  cv::Mat queryDescriptors;
  sift->detectAndCompute(img2, cv::Mat(), queryKeypoints, queryDescriptors);

  cv::Ptr<cv::DescriptorMatcher> matcher = cv::DescriptorMatcher::create("BruteForce");
  std::vector<cv::DMatch> matches;
  matcher->match(queryDescriptors, trainDescriptors, matches);
  std::cout << "matches[0]: trainIdx=" << matches[0].trainIdx << " ; queryIdx="
      << matches[0].queryIdx << " ; dist=" << matches[0].distance << std::endl;

  double my_dist = 0.0;
  for(int j = 0; j < trainDescriptors.cols; j++) {
    my_dist += (trainDescriptors.at<float>(matches[0].trainIdx, j) - queryDescriptors.at<float>(matches[0].queryIdx, j))
        * (trainDescriptors.at<float>(matches[0].trainIdx, j) - queryDescriptors.at<float>(matches[0].queryIdx, j));
  }
  std::cout << "my_dist=" << cv::sqrt(my_dist) << std::endl;