People need to stop confusing or using rivalry and derby interchangeably.
Rivalry: A rivalry is the state of two people or groups engaging in a lasting competitive relationship. Rivalry is the "against each other" spirit between two competing sides. The relationship itself may also be called "a rivalry", and each participant or side a rival to the other. Someone's main rival may be called an archrival. A rivalry can be defined as "a perceptual categorizing process in which actors identify which states are sufficiently threatening competitors".
Liverpool vs Man United is a rivalry
Arsenal vs Man United is also somewhat a rivalry from the Fergie/Wenger days.
Derby (game): A derby is seen as a game in which two sides that are close together geographically play against one another.
A 'derby' is a match between local rivals. i.e. teams that are from the same city or the same part of the country. These local games have a special place in the hearts of fans and players.
Is ‘El Clasico’ a Derby?
Although they are stern rivals and matches between the pair are the most prestigious fixtures in Spanish football, the ‘El Clasico’ between Real Madrid and Barcelona is not considered a “derby” as the teams are not in the same locality.
However, Real Madrid vs Atletico Madrid is a Madrid derby, and Barcelona v Espanyol is a Barcelona/Catalonia derby (or derbi barceloni, as it’s otherwise known).
