After the first note is known, the two are mostly indistinguishable. A person with really good relative pitch can, once they're told what the first note is, immediately identify everything that comes after it, just like someone with perfect pitch would. The difference is that someone with perfect pitch don't even need to be told what that first note is.
(This means someone with perfect pitch can walk along a road and tell you the note played by a tyre squeal in the distance, whereas someone with merely really good relative pitch would need to also hear a single reference note within a few seconds or minutes (pitch memory varies between individuals) to do the same.)