What is the conceptual difference? i.e. when a new kind of message is introduced, how do you decide which kind it will be? I find the presence of two separate lists rather confusing and redundant.
Topic on Help talk:Notifications/Types
The first badge (red, "alerts") contains most important notification types: new messages on your talk page, mentions, etc. The second badge (blue, "notices") contains less important notifications: pages likes, message on other talk pages, etc. With that system, you know if you have to take an immediate action, or if it the notification is not that important and can be handled later.
This has been changed after a survey on all English and French speaking WMF wikis.
Two years later: heh, yeah, I'm used to it now. Usually red means "someone is yelling at you". Thanks.