Does Gmail or Mailgun manage all email or just WP email?

Hello there,
I have read through the instructions for WordPress not sending emails (fast enough), on this page on WPBeginner – https://www.wpbeginner.com/wp-tutorials/how-to-fix-wordpress-not-sending-email-issue/

I am confused about the remit of Mailgun. Does it send all the mail from the server – so for all @playimports.com.au email addresses or just the WP emails?

Likewise with Gmail. Does it manage all the emails from this domain?

Thanks so much for your help!
Sarah