Each type references an extended class of \Drupal\Core\Render\Element\FormElement. It provides the element's definition and additional functions. Each element defines a prerender method in the class that defines the input type attribute along with other additional attributes.

Each input defines its theme as input__TYPE, allowing you to copy the input.html.twig base to input.TYPE.html.twig for templating. The template then parses the attributes and renders the HTML.

Some elements, such as emails, provide validators for the element. The email element defines the validateEmail method. Here is an example of the code from \Drupal\Core\Render\Element\Email::valdateEmail:

  /** 
   * Form element validation handler for #type 'email'. 
   * 
   * Note that #maxlength and #required is validated by _form_validate() already. 
   */ 
  public static function validateEmail(&$element, FormStateInterface $form_state, &$complete_form) { 
    $value = trim($element['#value']); 
    $form_state->setValueForElement($element, $value); 
 
    if ($value !== '' && !\Drupal::service('email.validator')->isValid($value)) { 
      $form_state->setError($element, t('The email address %mail is not valid.', array('%mail' => $value))); 
    } 
  } 

This code will be executed on form submission and validate the provider's email. It does this by taking the current value and trimming any whitespaces and using the form state object to update the value. The email.validator service is invoked to validate the email. If this method returns false, the form state is invoked to mark the element as the one that has an error. If the element has an error, the form builder will prevent form submission, returning the user to the form to fix the value.