The American imperialism of the 1890s was in some ways similar to earlier expansionism, but was also different in important ways.
The major similarity between the two is that both were motivated in part by a desire to gain economic and political power. The US was, in both cases, trying to become richer and more powerful as a nation.
The major difference is seen in the idea of the "White Man's Burden." In the earlier expansion, there was no idea of civilizing the people whose lands were being taken. The Indians were to be pushed aside, not civilized. The Americans' superiority gave them the right to take the land but did not impose any special responsibilities on them.
By contrast, the expansion of the 1890s was in part based on (or at least justified by) the idea that the US would be helping the people whose lands it took. For example, the US argued that it would help bring civilization to the Filipinos and that this made it acceptable to deny them their independence.
Both phases of expansion were clearly motivated by a desire for power, but the later phase was also, at least to some degree, motivated by a desire to "civilize" the "backwards" people of the places the US took.