Travellers could be forgiven for mixing up Air China and China Airlines. Surely these must be the same national carrier? Not so. The first is the airline that flies the flag for Beijing; the second has its headquarters in the small island of Taiwan that lies off the mainland of China.

Working out which airline belongs to which side is simple, however, when compared with the fiendishly complicated relationship between the two, which remain technically at war more than 60 years after they split.

Politicians and peoples on both sides of the Taiwan Strait are hoping that the start of direct flights today will move them a step further away from hostilities. The risks are real.

The Communist leaders of the People’s Republic of China say that they are determined to recover the island that they regard as a renegade province — by force if necessary. They have deployed more than 1,000 missiles along the coast to be unleashed against its 23 million inhabitants should the self-ruled island attempt to declare formal independence.

To confuse matters, the island has called itself the Republic of China (ROC) since Generalissimo Chiang Kai-shek fled the mainland after defeat by Chairman Mao’s armies in 1949 and set up his own government. For decades, Mr Chiang and his successors said that their aim was to reconquer the mainland and bring it back under the ROC flag.

The two sides have grown apart steadily, however, at first in the absence of any contacts at all from the late 1940s until the late 1980s. Those differences gained momentum as the island introduced direct elections for president and parliament, becoming the first real Chinese democracy in 1996.

A thaw in relations in the early 1990s resulted in a flood of Taiwanese investment into the mainland and the island’s entrepreneurs are now estimated to be the biggest outside investors in China. Direct links — particularly transport —have been long banned by the Taiwanese Government, which feared that the island would be flooded by mainland visitors and infiltrated by Communist agents.

Suspicion has simmered in Beijing. The Communist Party has been anxious that increasing numbers of islanders see themselves as Taiwanese rather than Chinese. It staged military exercises around the island in the run-up to the 1996 inaugural presidential elections, firing missiles into the sea near by and prompting the United States to send an aircraft carrier to the region.

Nine years later, the Chinese parliament passed an anti-secession law allowing the use of force if the island moved towards independence. While barely a dozen countries recognise the Government in Taipei, that move triggered widespread international concern about Beijing’s more aggressive approach.

The response stunned Beijing into extending an olive branch to the Nationalist Party, which swept back to power in presidential elections in March.

Andrew Yang, a Chinese military specialist at National Sun Yat-sen University in Taiwan, described relations as the warmest in 60 years. He urged caution, however. “The next step depends on how much trust can be created between the two government authorities," he said. "If they both want to enhance the engagement this requires a lot of trust to be built and Beijing will want to evaluate the benefits.”

The next step may depend on panda diplomacy. Taiwanese authorities have said finally that they would be willing to accept a gift of two four-year-old giant pandas. The bears — Tuantuan and Yuanyuan, which run together mean “united” — were regarded as too political by the island’s previous government.

Times Recommends

• UN may halt 400-year-old 'freedom of the seas'
• Where the Rosetta belongs can’t be set in stone
• Gas deal on hold, but Ukraine may pay in the end