for new and returning players looking for exotics post Title Update 12 – A lot of info around here is out of date now, it’s “simpler” than it seems.
The wiki and info around here is many months out of date, and I've just spent hours confused and frustrated.
Very simply – the exotics are in the global pools now, so you don't need to farm X bosses and open world bosses any more say in NYC if you have WONY.
An exotic like, say, Lady Death SMG would only drop from world bosses during the season event it was introduced. Now though, it drops anywhere as its' part of the global loot pool.
So now to get Lady Death, you should just look at the map for targetted SMG areas and farm control points in that area, or do the missions with the SMG symbol (changes every day), weeklies to get your legendary caches as it's a chance to drop there too, as well as all end bosses in missions can drop them, as well as bounties, public executions etc in the targetted areas. You can get it from the open world bosses in NYC, you just no longer need to target them specifically.
Best way these days is to go to challenging difficulty and focus on the targetted loot area, doing bounties, CPs (+3 or +4) and events (public execution, propaganda etc) in that area and just cross your fingers. Then just rest the CPs and repeat – you won't get the yellow crates in the supply rooms until they reset each day.
Hard mode drops mainly purples, whereas challenging drops pretty much guaranteed golds as a minimum.
You can focus target bosses and missions for specific exotics that drop from certain factions, and you have to go through the steps to get say Chatterbox to drop if you've never got the plans before, but if you already have those then the exotics are in the global loot pool.
Really you just need to focus on targetted loot areas and get as many yellow/named kills as possible for drops and just hope.
Unconfirmed for me, but running missions on one difficulty and switching to another and retrying leads to a higher drop rate of exotics. Not sure if that still applies these days.