What specific groups of americans made their way west in the 1800s

Gold miners, possibly. Gold was discovered in 1848 in the American River near Sutter's Mill, California by John Sutter. When word was released about his discovery of gold, this caused a sudden influx of people into the California area and the West in general. They were hoping to "get rich quick."
Also, antislaveryites and proslaveryites moved somewhat west to Kansas and Nebraska since the issue of slavery was the be decided by popular sovereignty in these areas. (If they could get more people who supported the same platform as them, the issue would be decided in their favor.)

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