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GENERAL CHANGES
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Major battles are all revamped with completely different teams
Generic trainers in general are all edited, some with only 1 mon that is very powerful.
Generation 8 DLC and PLA Pokemon/moves have been added to the game.
There are many, many new items hidden all around the game. Look anywhere you think there could be an item hiding!
There is now a Remind option when inspecting Pokemon in your party. This allows you to reteach them any moves they have previously forgotten.
IVs no longer exist.
EVs are unable to be earned in battle or from items; your Pokemon instead gain EVs upon leveling up.
You can freely modify what stats their EVs are allocated to in the status screen.
Attack and Special Attack EVs have been merged into "Offense", which gives additional points in both stats.
Level caps are no longer tied to your badge count, it instead increases between most major battles. (Your current level cap can be viewed on your trainer card.)
Rare candies are not consumed if used on a Pokemon that is lower level than the highest in your party.
Rare candies can only be used to go 3 levels above your current level cap.
All Pokemon gain exp at the same rate, and gain exp while fainted. 
You cannot find Light Clay, Amplifield Rock, or any of the weather extending rocks while mining.
Vitamins can now be used to change your Pokemon's nature. (Protein allows you to change to attack boosting natures, etc)
Old Gateau allows you to change a Pokemon's Hidden Power type.
Wild Pokemon can no longer hold items.
Pokeballs have 100% catchrate.
All events for Starter Pokemon have been axed. A second starter can be picked at the lab post-fly.
All berry plants have a maximum yield of 1.
Repels now repel everything, including mons that are higher leveled than you.
Contents of Dept Store floors have been edited.

Use PC is now in the CyberNav
Heal Party is now in the CyberNav

There is now an "ultra turbo". Hit F to enable it. It generally only increases speed in battle, doesn't work well for movement.

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BATTLE CHANGES
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#GENERAL

Enemy Pokemon will sometimes have a green Crest symbol by their health bar. This symbol means they have all of their abilities active at once ("Pulse 3").
For example, a Pulse 3 Oranguru will have Telepathy, Inner focus, and Symbiosis all at once.

Flinches, parahax, freeze and confusion self-hit cannot happen on the first turn of the battle, except by Fake Out. (Credit to DemICE for this system from Urmumium)

New system for stat boosting moves: 
Player Pokemon now have a default of +0 stat stages in each stat.
Increasing your stats via move, ability, or any other way will now grant a one time increase to your total stat stage limit (still maxing out at +6)
For example: If you use the move Dragon Dance, you will increase your maximum attack and speed stages to +1 each, and get +1 in both of those stats as usual.
Using Dragon Dance again while at +1 in those stats will not increase them further, but you can use it to restore those stats if they get lowered.
Enemy Pokemon do not have these restrictions.
Hail now boosts the defense of all Ice types by 50%.

#ITEMS

Razor Fang boosts biting moves by 20%.
Razor Claw boosts weak moves (60 bp or lower, like Technician) by 20%. Does not work with priority moves.
Lucky Punch boosts punching moves by 20%.
Bright Powder boosts light-based moves by 20%.
Quick Claw boosts priority moves by 20%.
Power Herb is no longer consumed upon use.
Lax Incense allows makes the holder skip the recharge turn of moves.
Pure Incense makes the holder immune to flinching.
Figi/Aguav/Wiki/Iapapa berries heal for 50% again.
Enigma Berry has a new effect: Drops the attacking stat of the opponent, depending on what category of move they hit you with. 

Castform Crest now gives Water Bubble instead of Rain Dish in the rain form.
Skuntank Crest fixed to give a 20% boost to both offenses.

#ABILITIES

Mega Launcher now boosts Fire Blast and Flash Cannon
Fairy Aura now additionally has the effect of Friend Guard.
Dark Aura recovers 1/6th of the damage you deal while attacking.
Iron Fist now boosts punching moves by 30% rather than 20%.
Inner Focus now additionally protects your partner from flinching in doubles.
Merciless now works with all statuses.
Synchronize now cures your status when it activates.
Anger Point now raises both offenses.
Snow Cloak now boosts special defense by 50% in hail, instead of giving evasion.
Sand Veil now boosts defense by 50% while in sand, instead of giving evastion.
Stall now makes an extra turn pass each turn, with no battler being able to pick an action.
Pickup now restores the Pokemon's held consumable item at the end of the battle, if the Pokemon did not faint. The old effect is gone.
Suction Cups now lowers the opponent's speed upon getting hit by a contact move.
Flower Gift now additionally boosts Sp Attack.
Flower Veil now grants Grass type STAB (like Steelworker).
Bad Dreams now grants immunity to sleep.
Ice Body now heals for 1/8th HP per turn.
Rivalry's downside is removed.
Damp is now a Fire version of Storm Drain, with no offensive boosts.
Corrosion now lets Poison type attacks hit Steel types for Super Effective damage.
Steam Engine now boosts speed by 2 stages.

#MOVES

All moves that are 90% accurate or above are now 100% accurate. Some moves that are 85% accurate are now 100% accurate.
Some Gen 8 DLC moves have been added.
+1 Critical hit chance is now 25% instead of 12.5%, except on Glitch Field.
Encore can only be active on one opponent at a time in doubles.
Drill Peck, X-Scissor, and Dragon Claw are now moves with +1 crit.
Follow Me and Rage Powder have 1 more priority.
Dragon Rush is now 100% accurate.
Crabhammer now has a 10% chance to lower defense.
Eruption now has a 10% chance to burn.
High Horsepower now has a 10% chance to flinch.
Spirit Shackle now works like Shell Sidearm.
Sucker Punch now never fails for the AI. However, it is halved in power if you switch.
Thunder Raid is now super effective on Ground types.
Jaw Lock is now Rock type.
Meteor Mash is 100 BP
Arm Thrust is 20 BP
Petal Blizzard no longer hits your partner.