Short answers, pulled from the story.
Official diplomatic relations between the United States and China began on the 1st of January 1979. President Jimmy Carter declared this change in a historic statement delivered to the press on the 15th of December 1978.
The 1979 agreement terminated U.S. recognition for the Republic of China in Taiwan. This decision required the immediate withdrawal of all American military personnel from the island nation and the cancellation of the Sino-American Mutual Defense Treaty.
Vice Minister Zhang Wenjin insisted on changing the Chinese translation to mean recognize instead of acknowledge to match the stronger English word recognizes. Deputy Secretary of State Warren Christopher later admitted that U.S. officials were aware of this alteration during negotiations but James Stapleton Roy remained silent about the discrepancy.
The Taiwan Relations Act allows the United States to sell defensive weapons to Taiwan under specific conditions despite the end of formal diplomacy. The legislation ensures continued commercial and cultural relations through the American Institute in Taiwan while preserving the ability to respond to threats against the island without direct military intervention.
Successive U.S. administrations maintain that only the English text is binding for their government because acknowledging a position does not equal agreeing with it. Washington regards the word acknowledge as determinative based on statements made by Warren Christopher at a Senate hearing questioner in 1983.