I'll give you one more clue - every commercial brewery whirlpools then chills!
Reason being we want to remove Hot Break (the matter that settles during the boil) and we really don't care about Cold Break (flock that forms during cooling). Cold break is an important source of nutrients for the yeast. Problem is that if you chill first, it is very difficult to discriminate between the two types of flock, Cold Break is also very fine and very slow to settle so eliminating it is both difficult and expensive in terms of wort losses.
In very high protein worts (6 row malt, lots of adjunct...) there can be so much cold break that it can cause problems (yeast coating, reduced bitterness...) but outside the US where they may use crappy malt, given a decent boil and a kettle fining, best practice is to either: -
Separate then cool, ignore cold break that forms post chilling, or
Chill with an immersion chiller, then make sure you leave enough wort in the kettle to ensure that all the hot break and hop trub stays in the kettle.
It would be a good idea to do a trial run if you are going to use an immersion chiller, syphon or otherwise transfer the hot wort from the kettle until you have clearly identified how much trub/wort you need to leave in the kettle to be sure that the hot break is left behind.
Mark