The message in a delivery email can come from three places. Each one overrides the one before it:
The template's message: the starting message for every video or presentation that uses that template.
The content's message: a message saved for one video or presentation, used for every delivery of it.
This delivery's message: what you type when you send.
When you send a delivery
The Message box on the Email Delivery form starts with the content's message, or the template's message if the content has none. Edit it for this delivery, or clear it to send no message.
To keep your edit for the next deliveries of this content, tick Use this message for future deliveries of this content.
To go back, use Reset to template message or Reset to this content's message. Stop using a custom message removes the message saved for this content, and the template's message is used again.
Changing the message never changes the email design.
Set a content's message
Open the video or presentation, choose Settings > Branding, open the Emails tab, and click Edit message. The line beside it tells you which message is in use: the template's, a custom one, or none.
When a template's message changes
When you save a template with a new message, content that uses the template's message shows the new one. You'll be asked about content that has a message of its own, and it keeps its own message unless you choose otherwise.
To edit a template, see How do I customize my Email Delivery design and branding?