The Event Email option allows you to send an email to event registrants. It's the same thing as when you click "email registrants" from the Event list. It is like a broadcast in that you can create a custom message, but the audience is restricted to registrants for specific event shifts.
The Promotion tool allows you to email all users or certain teams or groups an advertisement for an event. It is like a broadcast in the way you can target messages to users but it automatically pulls in the Event details rather than letting you customize an email.
