Shifts have their own lateness and non-attendance reasons. These work alongside the absence policy types but can also be used to record other information (such as lateness or approved early finish).
The options are controlled under System > HR Settings > Non-attendance Reasons.
You can create a non-attendance reason by clicking the ‘Create Attendance Reason’ in the Actions bar. For each reason, you can enter a title, the level (e.g. how severe the non-attendance was) along with choosing an icon.