When comparing US and European imperialism, it is notable that there are some similarities and some differences between the two.
When we look at European imperialism during the 1500s–1900s, it often involves the taking of a nation by military force. Countries like Britain, Spain, and France developed empires through this method. European nations utilized their military and technology superiority to conquer foreign lands. Once conquered, they would install a governor/governors to manage the territory in the name of the home country.
When we look at American imperialism, particularly in the more modern sense, it is a bit different. The US government generally doesn't just send in the military to conquer a nation and then install a governor to manage the territory. This strategy may have been more common in the past, such as the taking of Cuba and Puerto Rico during the Spanish-American War, or the taking of Hawaii, but more modern examples are less direct. The type of imperialism the US seems to engage in these days involves supporting and assisting leaders who the US favors over those that they don't. The United States will provide financial and military supports to leaders who support US policies on the global level or will provide beneficial deals for US corporations to operate inside their borders.
American imperialism may also involve the US government threatening other nations through economic means. The threat of cutting off trade with or raising tariffs on goods from other nations can be effective in getting them to cooperate with US goals.
When we look at motives for European and American imperialism, we will notice more similarities. In both cases one of the major goals of imperialism is not just the control of a territory, but access to the resources that territory holds. Gaining free or cheap access to these resources allows for extraction and usage in the home country. The added benefit of colonization is the utilization of the colony as a market for goods produced in the home country. So essentially the valuable resources are extracted, manufactured into finished products, and then sold back in the colonies for a profit. This strategy proved effective in gaining wealth for imperialist nations.
Another similarity between European and US imperialism would be the spreading of cultural values. In the age of European imperialism, one of the major goals was the spreading of Christianity. After invading and conquering a foreign nation, missionaries often arrived to spread Christian beliefs. The ethnocentric views of Europeans at this time felt that it was a duty to spread Christianity to the "uncivilized" people they had conquered. In a way they felt they were improving them by pushing European cultural and religious values on them.
This can also be seen in different ways through US imperialism. Although it may not be strictly based on spreading Christianity, the US does seem to push values of Western culture and American culture on foreign nations it aims to control. This can include the introduction of American forms of entertainment, dress, and other cultural aspects.