The Twins used to be the Senators, who used to go by the "Nationals." It's really not that confusing. It's like when the Athletics go by "A's", the Yankees go by "the Bombers", or the Red Sox go by "GODDAMMIT WHAT KIND OF PITCH WAS THAT?" So, if you want to be a lawyer about it, the Nationals haven't just made the playoffs already; they've been to the World Series and won it.
Over at DC Sports Bog, they've found some front-page articles from the Washington Post after the pennant-winner in 1924.
Cronin Eludes Mob of Women in Chase After Nats Clinch Pennant
They don't make headlines like that anymore.