I decided that the key distinction is that in the real world, things tend to happen for explicable reasons. Much less so in dreams. Usually when awake you can reconstruct the cause-and-effect chain which led to an event, but in dreams they are often omitted, and in the midst of the dream we're cool with that.
Dreams are valuable because they drop us in hypothetical situations and let us see how we'd behave. How might you act if your best friend refused to talk to you for no reason? What if you married your ex? How would you survive a zombie apocalypse? We can only gain the insights these dreams give us because we're willing to put aside the question "why is this happening?"
But there's a problem with this distinction: in real life, things happens for no good reason all the time. Super-fit health nuts die of cancer at 30 while obese alcoholics live to 100. Millions have been brutally killed in war crimes ordered by dictators who die comfortably in their beds. Goodness is exploited and greed is rewarded and nobody has a good answer to the question "why?" To get by in this life, you have to live with leaving the question unanswered. You can either believe that there is no reason, or that there is some unknowable reason and hopefully someday you'll be let in on the secret.
So this leads to the obvious question: what if this life is just a dream? What if the real world is a place where everything happens for a good reason, and the reality we know is just a place where our minds can experiment with the question, "what if bad things happened to good people?" What if, to our waking selves, the random misfortunes that befall the good are as outlandish as flying humans, or talking animals, or accidentally getting on a nonstop bus to China? And what if our visions of Heaven and Hell are just distant memories of what the waking world is really like?