I don't know if other people think about these conventions in the same way I do but the way I see them is.
Notice: Simply a statement that is non-actionable, use these to alert the user of something smaller and passive that you want the user to notice, such as an event that has happened like a successful submit.
Info: Actionable statement that you need the user to see and act on, but with no negative connotation (see Warning/Error), use this for things like "There is a new update to this Software"
Warning: Negative connotation, given before anything goes wrong but warns users of imminent problems if they proceed down a certain path. Such as "email left blank, you cannot submit without valid email".
Error: Negative connotation, given after something has already gone wrong, try to include what went wrong and how to fix said issue.
don't get me wrong these are subtle differences and could likely be used interchangeably but that is how I see them.