What is the difference between way US gained Alaska and Hawaii?

The United States gained Alaska through a purchase, while Hawaii was annexed.

Alaska

Alaska was purchased from the Russian Empire in 1867 for $7.2 million. The purchase was negotiated by Secretary of State William H. Seward and was approved by the U.S. Senate by a vote of 37 to 2. The purchase of Alaska was seen as a strategic move by the United States, as it gave the country a foothold in the North Pacific and control over the strategically important Aleutian Islands.

Hawaii

Hawaii was annexed by the United States in 1898. The annexation was the result of a series of events that began with the overthrow of the Hawaiian monarchy in 1893. The United States, which had significant economic interests in Hawaii, played a role in the overthrow and subsequently annexed the islands. The annexation of Hawaii was opposed by some Americans, who argued that it was an act of imperialism. However, the annexation was ultimately approved by Congress and signed into law by President William McKinley.