How is American imperialism of the late 1800's similar or different to today's foreign policy?
There are major similarities between these two foreign policies.
In each case, the policy was based on economic, military, and cultural/political ideas. The US wanted an empire in the 1800s in part so it could have access to raw materials. Current foreign policy is very concerned with keeping the world's oil supplies flowing. In the 1800s, the US wanted bases from which to project naval power. Today, we continue to want to project our power around the world. In the 1800s, we believed in the "white man's burden." Today, we still believe that we can and should bring democracy to places where it does not now exist.
The major difference is that we are much less aggressive about achieving these goals. We no longer simply take control over other countries. Cynics might say we do control them, but it is clear that we do not do things like making Iraq a US possession the way we did with the Philippines. Today, we try to use soft power as much as hard power. When we do fight, we try to do so for the benefit of other countries, not as a way to create an American empire.