WooCommerce has a variety of order notifications relating to orders placed within the system. New Orders, Cancelled Orders, and Failed Orders are the most common that site administrators expect to see. 

When a Customer gets to the checkout page, our payment plugins take over briefly and handle the negotiation with the processor.  

When we receive back a reply that indicates approval of the transaction, we alert WooCommerce that the order is ready to go and WooCommerce takes back over.  Typically this is when the Order Status is changed to Pending and the various emails are sent.  WooCommerce triggers and sends these emails, our software does not. 

Within WooCommerce, you can configure the email notification settings from within the Dashboard at WooCommerce > Settings > Emails ... as seen below:

Once you've found the email you want to change, you can edit the various settings from within each one by clicking on the blue title and modifying the settings on the editing page as seen below:

There are a number of third party plugins you can install to further modify your messaging. 

We also suggest configuring an SMTP mailer, such as 'The Postman' or 'Easy SMTP WP' to improve the deliverability of your messages.  By default WooCommerce is configured to send unauthenticated email which is the electronic equivalent of bulk / junk mail at the Post Office - it will frequently be marked as spam and may or may not ever make it to the recipient at all.