Sending an identical message in an e-mail blast to all customers is an example of

Broadcast message

Explanation:

A broadcast message is an identical message sent to a lot of recipients. When it is an email, it can be sent in Carbon Copy (Cc) or a Blind Carbon Copy (Bcc) form.

With the Carbon Copy, every recipients will be notified about the other recipients. In most cases all the email usernames of the recipients will be sent to all the recipients individually.

With the Blind Carbon Copy, every individual sees the message as he/she received it alone. The individual is not notified about the other recipients.