Different Types of Announcements

The announcement type has little to do with how the announcement looks, and more specifically determines the 'scope' of the announcement. By which we mean 'who' can see the announcement.

GlobalGlobal Announcements are shown to all authenticated Jira users and all Service Desk customers in all projects, and service desk portals.

The announcement will show on the System Dashboard (if you added our gadget), on the issue details screen, the service desk portal, and the service desk ticket screen.

Anonymous users, not authenticated to your Jira instance will not see Global announcements.
PublicPublic Announcements are only shown to anonymous users that have not authenticated to your Jira instance. This includes the System Dashboard, as well as issue details screens if your Jira instance is public.
CustomerCustomer Announcements are specifically scoped for Service Desk projects.

For these announcements, you select which service desk project you wish to make your announcement in, and which of the service desk screens should show it.

This type of announcement is not shown to your Jira users (neither globally, nor in the specific project you selected). Instead, it only shows to Service desk customers.