Version-exclusive Pokémon in Sword & Shield
Like all the paired games in the Pokémon series, Sword & Shield each include Pokémon that cannot be obtained in the alternate version. To obtain Pokémon missing from your version you need to trade with someone who has the opposite version.
All the exclusives are listed below. Note that Flapple and Appletun are not stricly version-exclusive, but the items required to evolve Applin are. Interestingly, there are also two version-exclusive gyms in Pokémon Sword & Shield: in Sword there is a Fighting type gym headed by Bea and a Rock type gym headed by Gordie; in Shield they are a Ghost type gym headed by Allister and an Ice type gym headed by Melony.
Exclusive to Pokémon Sword

Farfetch'd
Galarian Farfetch'd
Fighting

Darmanitan
Galarian Standard Mode
Ice

Sirfetch'd
Fighting

Stonjourner
Rock

Gothitelle
Psychic

Turtonator
Fire · Dragon
Exclusive to Pokémon Shield

Aromatisse
Fairy