FormInterface::validateForm() and FormInterface::submitForm() are always called

In Drupal 7, default form validate or submit functions were determined by appending _validate and _submit to the form ID.
However, these were not triggered if a custom #validate or #submit handler was used.
In which case, the default handlers needed to be specified manually.

Drupal 7

No custom submit handler

function test_form($form, $form_state) {
  $form['submit'] = array('#type' => 'submit', '#value' => 'Save');
  return $form;
}

function custom_submit_function(&$form, &$form_state) {
  // This would NOT be executed.
}
function test_form_submit(&$form, &$form_state) {
  // This would be executed.
}

Custom submit handler

function test_form($form, $form_state) {
  $form['#submit'][] = 'custom_submit_function';
  $form['submit'] = array('#type' => 'submit', '#value' => 'Save');
  return $form;
}

function custom_submit_function(&$form, &$form_state) {
  // This would be executed.
}
function test_form_submit(&$form, &$form_state) {
  // This would NOT be executed.
}

Custom submit handler and default specified

function test_form($form, $form_state) {
  $form['#submit'][] = 'custom_submit_function';
  $form['#submit'][] = 'test_form_submit';
  $form['submit'] = array('#type' => 'submit', '#value' => 'Save');
  return $form;
}

function custom_submit_function(&$form, &$form_state) {
  // This would be executed.
}
function test_form_submit(&$form, &$form_state) {
  // This would be executed.
}

Drupal 8

No custom submit handler

class TestForm extends FormBase {

  public function buildForm(array $form, array &$form_state) {
    $form['submit'] = array('#type' => 'submit', '#value' => 'Save');
    return $form;
  }

  public function submitForm(array &$form, array &$form_state) {
    // This would be executed.
  }

  public function customSubmitForm(array &$form, array &$form_state) {
    // This would NOT be executed.
  }

Custom submit handler

class TestForm extends FormBase {

  public function buildForm(array $form, array &$form_state) {
    $form['#submit'][] = array($this, 'customSubmitForm');
    $form['submit'] = array('#type' => 'submit', '#value' => 'Save');
    return $form;
  }

  public function submitForm(array &$form, array &$form_state) {
    // This would be executed.
  }

  public function customSubmitForm(array &$form, array &$form_state) {
    // This would be executed.
  }

Custom submit handler and default specified

class TestForm extends FormBase {

  public function buildForm(array $form, array &$form_state) {
    $form['#submit'][] = array($this, 'customSubmitForm');
    // Do not do this.
    $form['#submit'][] = array($this, 'submitForm');
    $form['submit'] = array('#type' => 'submit', '#value' => 'Save');
    return $form;
  }

  public function submitForm(array &$form, array &$form_state) {
    // This would be executed TWICE. Do not specify the default handler.
  }

  public function customSubmitForm(array &$form, array &$form_state) {
    // This would be executed.
  }