Can anybody explain to me why do they say in football terms, its a derby?

When two teams from the same town play against each other, it’s a derby. The fans are very polarized, sometimes the game is very important to them regardless of its effect on their place in the league. When Real Madrid plays against Barcelona, it’s also a derby. They’re not from the same town & it doesn’t matter if a 3rd team is winning the league. Those two teams had been rivals to each other for a century. For many fans, the game those 2 teams play against each other is a tournament by itself.