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Soul Bond & Partner Up, they are separate mechanics.
Soul Bond:
>two Pokémon fight as one by holding resonating stones for 3 turns
>this boosts out front Pokémon’s stats to have the highest stat of the Pokémon in back or being bonded to
>in doubles there is only one Pokémon on the field after bonding for one turn, then as if one died you send another out, and at the end of the 3 turn the bonded Pokémon usually returns to your party
>A fifth move is opened: if they are compatible, it will be entirely new (Charizard X Venusaur = Razor Lava). If not (ie banette and shuckle) it will pick the first move of the Pokémon in back (such as sticky webs)
>if the soul bonded Pokémon dies they are both dead
>after soul bond they will split and share the lowest HP, even if the lowest is the secondary bonded one
Partner Up
>Doubles only
>Pokémon combine efforts to attack more efficiently
>this includes each attacking separately, or a finale move which ends the partnership early
>HP is pooled and lost proportionately when attacked together, HP is separate when attacked separately.
>Each partner can be attacked separately (separate bulk and typing), or together (averaged bulk and combined typing), but Partner Up allows you to freely Ally Switch once per turn at the cost of one of their movements, except it fails to help if they target you as a whole
>there are two synergies
>Elemental: physical attackers can use fire, water, electric, dragon or ice as a secondary type with their move if it makes contact, special attackers can combine those elemental moves with physical contact moves that use defense if it is lower than special attack, but only with fighting, flying, normal, steel or rock type moves
>combining two moves may sometimes yield a unique move
>Forceful: the highest attacks and speed of both Pokémon are used when calculating damage whether they attack separately or together, however the lowest bulk of both of them are also calculated when attacked together.