I noticed that all labels in the "Activity Type Options" and "Custom Fields" cannot be the same. For example, if I wanted to add a "Medical Assessment" activity type, I cannot use the same label again. This matters, because when I assign this activity type to a specific case, I have custom fields attached to this medical assessment activity.
The problem is, when I create another case type and use "medical assessment" again, I want different custom fields to be attached.