Which core module provides the default send email action for use in rules? There is a core module (might be related to core actions) that allows your to send an email via VBO. What is the name or where is that function located in core?

For e.g. When I am modifying the system mail settings, what "module" in core provides this functionality? (See screenshot)
There is no "module", at least not one that can be turned on and off like other modules. Emails are normally handled by drupal_mail() and a bunch of other functions found in the system.mail.inc file under /modules/system and mail.inc found in /includes .  These work together to create the framework, using templates that you can set up in order for other modules (like VBO) to actually send emails.

drupal_mail():


  Sending an e-mail works with defining an e-mail template (subject,
  text and possibly e-mail headers) and the replacement values to use in
  the appropriate places in the template. Processed e-mail templates are
  requested from hook_mail() from the module sending the e-mail. Any
  module can modify the composed e-mail message array using
  hook_mail_alter(). Finally drupal_mail_system()->mail() sends the
  e-mail, which can be reused if the exact same composed e-mail is to be
  sent to multiple recipients.