Compare and contrast the acquisition of Texas and the Southwest with the annexation of Oregon.
The main difference here is the means by which these territories were acquired, and who we were competing with for that territory.
The Oregon Country was acquired through treaty with the British, after a short period of harsh words between then President James K. Polk and the British government. No shots were fired and a compromise treaty settled things permanently.
In the case of Texas, it was annexed by the United States for the primary reason of provoking Mexico into war. To do so we annexed more than Texas, but all the way to the Rio Grande River, much further south, so Mexico would have no choice but to fight. So this land was acquired through war. the Mexican-American War lasted from 1846 - 48 and also ended by treaty, but this time it was signed at US gunpoint and a much larger chunk of land, the Mexican Cession, was seized than in the Northwest.
Still, it can be said of both territories that it got us to the Pacific Ocean as a nation, and achieved the long held goal of Manifest Destiny.