Earthquake and Tsunami Warning Service: is a service that delivers Earthquake and Tsunami Warning Notifications provided by Warning Notification Providers to the UEs which have the capability of receiving Warning Notifications within Notification Areas through the 3GPP network.
Earthquake and Tsunami Warning System: is a subsystem of Public Warning System that delivers Warning Notifications specific to Earthquake and Tsunami provided by Warning Notification Providers to the UEs which have the capability of receiving Warning Notifications within Notification Areas through the 3GPP network.
Earthquake and Tsunami Warning service is provided to users by PLMN operators. Warning Notification Providers produce Warning Notification to PLMN operator when an event occurs e.g. an Earthquake. PLMN operators distribute Warning Notifications to users by utilizing ETWS.
The ETWS consists of the PLMN that is capable to deliver Warning Notification and the UEs that are capable to receive Warning Notification. A Warning Notification Provider is able to send Warning Notification to the users in Notification Area by activating ETWS. Warning Notification is classified into two types depending on the purpose and urgency of the notification.
The first type of Notification is called Primary Notification. This type of notification delivers the most important information of the threat that is approaching to users (e.g. the imminent occurrence of Earthquake or Tsunami). The notification shall be delivered to the users as soon as possible.
The second type of Notification is called Secondary Notification. This type of notification delivers additional information, such as instructions on what to do / where to get help as long as the emergency lasts.
More Information at 3GPP TS 22.168: Earthquake and Tsunami Warning System (ETWS) requirements; Stage 1.
You may also find interesting this FAQ for Cell Broadcast (CB) in Public Warning.