The KMT originated as a Nationalist movement in the early 20th century that controlled much of China. After losing a civil war with the Chinese Communist Party, the KMT re-established itself in Taiwan. It very much favors eventual unification with the mainland, and it often focuses on economic ties between the two states. The DPP is a newer political party that emphasizes Taiwan's unique identity and independence after many Taiwanese grew tired of decades of military rule by the KMT. The DPP is the current ruling party, but presidential elections will be happening again next year.
During President Tsai's visit to the U.S., former president and KMT member Ma Ying-Jeou was also touring Mainland China, fervently supporting a One-China unification. The two trips could not have been more different, and they represented two futures for Taiwan. Economically, Taiwan and China are very interconnected. Many companies operate in both countries and trade is high. While China is very open to Taiwanese visitors, Taiwan keeps a very strict watch on Chinese visitors.
However, the 2020s will inevitably mark a sharp turning point in relations between the two countries according to many regional experts. The latest drills are a sign of that. Many people who support an independent Taiwan are afraid that an invasion by China is imminent, so U.S. and East Asian policymakers are working around the clock to discourage that from happening. As rising energy and food prices from the War in Ukraine have shown, issues in far-off areas of the world can affect us at home.