Welcome and Pending emails can be configured within CB > Configuration > Registration.

bins wrote: Not the admin email!

I am using CBSubs - does that make a difference?

Please paste a sample of what you are referring to as "admin email".

bins wrote: Apologies, I did not check on what my colleague told me!

Admin is receiving confirmation emails of new members. Part of the email uses the [DETAILS] as a substitution, however, when admin receives a copy, it does not show the members details, but the site registration email and from email name.

I really need exact email contents to give you a complete answer.

Pending approval emails are sent to moderators based on the language string configuration in your language plugin.

If you install the English language plugin from here:
forge.joomlapolis.com/projects/lan-cb-en/files

you can see the pending approval emails and the new user emails that are sent to moderators in the language.php file:

'UE_REG_ADMIN_PA_SUB' => 'ACTION REQUIRED! New user sign up request pending approval',
'UE_REG_ADMIN_PA_MSG' => "A new user has signed up at [SITEURL] and requires approval.\nThis email contains their details\n\nName - [NAME]\nE-mail - [EMAILADDRESS]\nUsername - [USERNAME]\n\n\nPlease do not respond to this message as it is automatically generated and is for informational purposes only.\n",
'UE_REG_ADMIN_SUB' => 'New user sign up',
'UE_REG_ADMIN_MSG' => "A new user has signed up at [SITEURL]. at [SITEURL].\nThis email contains their details\n\nName - [NAME]\nE-mail - [EMAILADDRESS]\nUsername - [USERNAME]\n\n\nPlease do not respond to this message as it is automatically generated and is for information purposes only\n",