In the case of these emails, you need to copy
/includes/languages/english/checkout_process.php to
/includes/languages/english/[custom]/checkout_process.php.
Another file, which contains most of the purchase confirmation verbage is
/includes/languages/english/html_includes/define_checkout_success.php. Copy this to /includes/languages/english/
[custom]/html_includes/define_checkout_sucess.php and modify to your liking.
Note: Replace [custom] with the actual name of your custom template...and be sure to use the same name for all folders containing custom template files. Note: You may already have a custom template in use. (check admin tools-->select template screen to find out.) If so place the files in folders with that name.
If you did not have a custom template already established, then you will need to activate your new custom template in admin at Tools -->template selection. You do not need to copy all default template files to your custom template folders. Only generate custom files you need to modify your site. Checks for custom files first and if a specific file is not found, it uses the default file.