Neither of these are really specific. They don't add meaning to the questions.
My first two thoughts when reading this title were "What the heck does that mean?" and "Why would we ever need those two words?"
I'd like to quote the other question:
The error message still appears in a certain program, so it should be sufficient to tag it with that. Think about it: Would anybody ever follow error-message, because they're an expert in… error messages?
I personally don't know any expert in alerts or warnings, so I assume the same arguments are valid in this discussion.
You would differentiate between the two if there are different severities for the error/warning/alert/info. http://msdn.microsoft.com/en-us/library/aa937483%28v=sql.80%29.aspx?ppud=4 has a gazillion levels, which can be useful to a user who wants to filter out severities below a given level. You would lower the severity threshold when you want to get every last warning out; raise the threshold if you have to get something out quickly and don't have time to sweat the details.