Damage Categories (Physical and Special)
Damage categories describe whether a move uses Attack and Defense or Special Attack and Special Defense. The category matters more than the move's type.
Physical vs Special
Physical moves use the attacking Pokemon's Attack against the defending Pokemon's Defense. Special moves use the attacking Pokemon's Special Attack against the defending Pokemon's Special Defense. Status moves do not deal direct damage. If two moves share a type, one can still be physical while the other is special.
How the category is chosen
In modern games, the category is set per move. Before Generation IV, the move's type decided the category, so older games need generation context when you compare damage.
Common exceptions
Some moves do not follow the usual stat pair. Body Press uses Defense as the attacking stat, Foul Play uses the target's Attack, Psyshock and Psystrike hit Defense while still being special moves, and Tera Blast changes category based on the user's higher attacking stat when it can.
Battle impact
The physical/special split decides which stat pair matters, which in turn changes how you build a Pokemon. A fast physical attacker wants different EVs and natures than a bulky special attacker, even if both use the same type chart.
FAQ
When was the physical / special split?
The physical / special split took place in Generation IV. Prior to Generation IV, every move of a specific type always had the same damage category.
Which types were physical and special before the split?
Normal, Fighting, Flying, Poison, Ground, Rock, Bug, Ghost, and Steel were physical. Fire, Water, Grass, Electric, Psychic, Ice, Dragon, and Dark were special.