In the LMS, you will see terms like "notification" and "alert" scattered in a variety of locations from calendar to content elements on your homepage! So, what's the difference?
Notifications: Updates the members' Activity Stream within the group space.
Alerts: Updates the Activity Stream AND sends an email or text message to those who have signed up for them!
Here is an example of where you will see the option to send notifications (usually located below the element by the update/save button):
Group space overview, content areas on the homepage or updating a resource.
You will see the option for members to sign up for alerts (the blue button) on calendars, blogs, and discussions.
Each individual member of the group space, has to sign up for alerts on their own. If you would like each student to sign up for alerts from your class it might be best to walk the students through it so you can ensure they have all signed up!