Here's some I know:
Barrier and Iron Defence are the same.
Aeroblast and Spacial Rend are the same.
Cross Chop and Stone Edge are the same.
Leaf Blade and Attack Order are the same.
Accelerock, Quick Attack, Bullet Punch, Aqua Jet, Ice Shard, Mach Punch, Shadow Sneak, and Vacuum Wave are the same.
Fury Attack and Barrage are the same.
Bullet Seed and Icicle Spear are the same.
Arm Thrust and Pin Missile are the same.
Rock Blast and Bone Rush are the same.
Defend Order and Cosmic Power are the same.
Dragon Assent and Close Combat are the same.
Earth Power, Energy Ball, Bug Buzz, and Psychic are the same.
Detect and Protect are the same.
Crunch, Shadow Ball, and Flash Cannon are the same.
Giga Drain, Drain Punch, and Horn Leech are the same.
Eruption and Water Spout are the same.
Fleur Cannon, Draco Meteor, Leaf Storm, and Overheat are the same.
Soft Boiled, Heal Order, Recover, and Milk Drink are the same.
Ice Hammer and Hammer Arm are the same.
Outrage, Thrash, and Petal Dance are the same.
Precipice Blades, Megahorn, and Power Whip are the same.
Night Shade and Seismic Toss are the same.
Fire Fang, Ice Fang, and Thunder Fang are the same.
Fissure, Guillotine, Horn Drill, and Sheer Cold are the same.
Fire Pledge, Grass Pledge, and Water Pledge are the same.
Acid, Bubble, Ember, Thunder Shock, and Powder Snow are the same.
Ancient Power, Silver Wind, and Ominous Wind are the same.
Bubble Beam, Psybeam, Spark, Aurora Beam, and Sludge are the same.
Bite and Heart Stamp are the same.
Blizzard, Thunder, and Hurricane are the same.
Bolt Strike and Blue Flare are the same.
Brine, Hex, and Venoshock are the same.
Bug Bite and Pluck are the same.
Catastropika (Z-move) and Pulverizing Pancake (Z-move) are the same.
Circle Throw and Dragon Tail are the same.
Whirlpool, Clamp, Fire Spin, and Rock Tumb are the same.
Mirror Coat and Counter are the same.
Wring Out and Crush Grip are the same.
Crush Claw and Razor Shell are the same.
Dig and Dive are the same.
Discharge and Lava Plume are the same.
Dynamic Punch and Inferno are the same.
False Swipe and Hold Back are the same.
Fire Lash and Lunge are the same.
Fire Punch, Thunder Punch, Ice Punch, Signal Beam, and Relic Song are the same.
Flail and Reversal are the same.
Flamethrower, Ice Beam, and Thunderbolt are the same.
Frost Breath and Storm Throw are the same.
Frustration and Return are the same.
Fusion Bolt and Fusion Flare are the same.
Gust, Pound, Tackle, Fairy Wind, Scratch, and Leafage are the same.
Gyro Ball and Electro Ball are the same.
Heavy Slam and Heat Crash are the same.
Hyper Beam, Blast Burn, Frenzy Plant, Hydro Cannon, Giga Impact, Roar of Time, and Rock Wrecker are the same. Icy Wind, Mud Shot, Electroweb, and Snarl are the same.
Karate Chop and Poison Tail are the same.
Liquidation and Shadow Bone are the same.
Low Kick and Grass Knot are the same.
Luster Purge and Mist Ball are the same.
Moongeist Beam and Sunsteel Strike are the same.
Needle Arm and Force Palm are the same.
Octazooka, Mud Bomb, and Mirror Shot are the same.
Avalanche and Revenge are the same.
Rollout and Ice Ball are the same.
Sky Attack, Freeze Shock, and Ice Burn are the same.
Night Slash, Psycho Cut, Shadow Claw, Slash, and Cross Poison are the same.
Smelling Salts and Wake-Up Slap are the same. Synthesis, Morning Sun, and Moonlight are the same.
I'll put more once I find them. I didn’t put the recoil moves because you already know what they are.