All Pokémon games released in pairs have minor differences between them, and Pokémon Sword & Shield are no different. Some details here are speculative—the page will be updated after the release of the games with concrete information.
Version Exclusive Pokémon
Each game is home to Pokémon species not found in the other. To collect all the Pokémon in Galar, you’ll need to trade with friends or buy both versions.
Pokémon Sword Exclusives
Galarian Farfetch’d and Sirfetch’d
Galarian Darumaka and Galarian Darmanitan
Deino (plus its evolutions Zweilous and Hydreigon)
Jangmo-o (plus its evolutions Hakamo-o and Kommo-o)
Gothita, Gothorita, and Gothitelle
Rufflet and Braviary
Pokémon Shield Exclusives
Galarian Corsola and Cursola
Galarian Ponyta and Galarian Rapidash
Larvitar (plus its evolutions Pupitar and Tyranitar)
Goomy (plus its evolutions Sliggoo and Goodra)
Solosis, Duosion and Reuniclus
Vullaby and Mandibuzz
Exclusive Legendary Pokémon
Zacian will be exclusive to Pokémon Sword, while Zamazenta will be exclusive to Pokémon Shield.
Version Exclusive Characters
Currently this section should be considered very speculative in nature outside of Bea and Allister.
Pokémon Sword Characters
Bea is a Fighting-type Gym Leader exclusive to Pokémon Sword
Gordie is a Rock-type Gym Leader exclusive to Pokémon Sword
Pokémon Shield Characters
Allister is a Ghost-type Gym Leader exclusive to Pokémon Shield
Melony is an Ice-type Gym Leader exclusive to Pokémon Shield