Supposedly, liberal democracies have never fought against one another on the battlefield. During the second World War however, Finland was using the Molotov cocktail and Nazi Germany to keep the Soviets out of their country, thereby fighting with an English enemy against an English ally. This development led to England declaring war on Finland, and producing the incredibly rare occurence of a liberal democracy declaring war on another liberal democracy.
The Soviet Union had eyes on Finland and right after Hitler invaded Poland, Stalin invaded Finland. The Finns were outnumbered three-to-one yet managed to stay independent even though they had to cede valuable land to the Soviets in an agreement made in 1940. Not surprisingly considering how outnumbered the Finns were, they managed to keep the Soviets at bay by employing guerilla tactics, and in the process, develop the Molotov cocktail after adapting an incendiary device used in the Spanish Civil War by the Russians.
The Finns named the cocktail a Molotov to mock the then Soviet Union's Secretary of War who publically declared that the Soviet Union was not dropping bombs on Finland, but in fact delivering food. So the Finns mass produced their own adaptation of a Russian incendiary device, and sent back to the Soviets the food they had been delivering in the form of Molotov cocktails.
After the peace treaty of 1940, the Finns were smart enough to realise that the Soviets would again try to conquer their country in the near future. Knowing that alone they would not be able to stand up to the might of the Soviets indefinitely, they vainly sought for help from Sweden and England. This help was not forthcoming due to both tactical and diplomatic reasons, and so a deal was struck with Nazi Germany for supplies and access to Finnish territory in order to keep the Soviets out, and to regain the territory Finland had lost in the peace treaty of 1940.
So being that Finland was allied with the Germans and fighting the Soviets, England reluctantly declared war on the Finns mostly as a means to sustain a workable relationship with the Soviet Union. The British RAF execution of an air raid on a Finnish harbour was about the extent of actual fighting that occurred between the two countries however. Nonetheless, one liberal democracy not only declared war on another liberal democracy, but actually attacked its territory.
Anyway, the Finns managed to defend their territory without eventually regaining their losses from the peace of 1940. In the end, they had to chase the Germans out of their country after a second peace treaty had been negotiated with the Soviet Union, and although fighting against the victors of the War, international opinion was sympathetic to Finland's position and its well regarded reputation in world affairs was unaffected.
Most of the information can be found at Wikipedia. Look here: https://en.wikipedia.org/wiki/Continuation_War