Darker and Edgier vs. DeconstructionDeconstructions are often Darker and Edgier because they take a typical genre or trope and examine the likely implications of that trope that straight uses tend to ignore in the interests of Escapism. Playing with a trope in this way is potentially a potent way to reveal the underlying Fridge Horror of a trope or genre. Thus a cartoon version of the medieval princess becomes grittier and less colorful. However, the converse is not true; making something darker and edgier isn't necessarily a deconstruction.
If the princess is raised in a restrictive environment due to her gender, becomes a pawn in international politics, and learns to keep her head above the water by playing political intrigue using feminine wiles and her position of influence with powerful people, this is a deconstruction.
If the kingdom is invaded by a brutal neighboring nation, the royal family's murder described in Gornful detail, and the princess repeatedly raped before being sold into slavery, this is Darker and Edgier but not a deconstruction.
Simultaneously, deconstruction can come about by making something Lighter and Softer, demonstrating that playing theoretically dark tropes in a lighter manner doesn't diminish the impact they can have on the story. Or in using Played for Laughs it points out the ridiculousness of darker tropes even in a realistic setting. Or even Played for Laughs by pointing out why these dark tropes and ideas would fail in the reality of that universe.
Subversion vs. DeconstructionAgain, these two aren't mutually inclusive. When a trope is deconstructed, its consequences are subverted by playing them true to life rather than going with the conventional depiction, but not all subversions are deconstructions.
- Tap on the Head played straight: A character is rendered unconscious with a blow to the head, with no ill effects afterward.
- Subverted: For laughs - ":thump: Ow! That hurt! What'd you do that for? :thump: Stop hitting me! :thump: [attacks]"
- Deconstructed: The character hit isn't rendered unconscious, but severely concussed, still capable of limited movement or slurred speech, but not of resisting. He spends days with fuzzy vision and headaches.
When an entire genre is deconstructed, it's usually not a subversion. Watchmen and Kingdom Come deconstructed superheroes by giving them realistic and often unfortunate motivations, goals, and results, but both made clear from their opening pages that these were not your grandparents' comic book stories—they weren't subverting the genre because they never purported to be a straight example of the genre in the first place.
Aversion vs. DeconstructionThere are a lot of tropes out there that are necessary to some kinds of fiction. When a woman in a bodice ripper gets kidnapped by pirates and ends up falling in love with her lusty, bearded, Byronic hero, you'll probably notice that she's surrounded by The Pirates Who Don't Do Anything.
In an historical novel, she will be travelling on an India-bound member of the merchant fleet before their ship is attacked by corsairs who torture the crew for their valuables, force the ship's carpenter, cooper, and smith to join their crew, and then kidnap her for good measure. She is most definitely not surrounded by The Pirates Who Don't Do Anything.
Some tropes hold up certain genres (a story set in a court that isn't full of deadly intrigue probably won't be interesting), others are handwaves or Plot Holes that we accept for the sake of the story. A genre deconstruction, by making the story more realistic, will tear these tropes to pieces or simply abandon them. Thus a genre deconstruction may often entail averting some tropes typical to the genre.
However, deconstructing a trope by itself doesn't entail averting the trope. Quite the opposite; deconstructing a trope means the trope is played even straighter than normal and its consequences or cause are explored in detail, usually for the purpose of irony, satire, or straight up horror.
Inversion vs. DeconstructionAn inverted trope is one that's turned on its head, played back to front. A High-Heel–Face Turn might be inverted by The Chick of the Five-Man Band being seduced to evil, or the lone man working with a group of female villains might come to the side of good.
A deconstruction would instead play the trope as straight as possible to explore how it might play in reality. The lone female villain might switch sides because, let's face it, are bad guys likely to be feminists who respect her opinions and give her equal pay? Or perhaps she was just arm candy and never really paid attention to what her boyfriend was doing. Or it turns out the heroes don't ever trust her because, used to be evil + betrayal = why would they?
Reconstruction vs. DeconstructionThe difference between reconstruction and deconstruction depend largely on what the end goal becomes. A deconstruction is about demonstrating the flaws of a trope or genre and leaves it at that. It is a situation that has no easy out. A reconstruction offers a solution on how to fix the situation via the repairs to the characters and story.
In many cases a reconstruction is a deconstruction of the original deconstruction, pointing out the flaws of the deconstruction and why that doesn't have to be the end result. Some works, naturally, will try to do both at the same time; deconstructing the original premise to reconstruct a new, more logically consistent solution at the end that still fits the spirit of the original pattern.