The wild west had two phases. Before the railroads reached Missouri and Kansas was the time of the mountain men that traveled up rivers as far as the North Fork of the South Platte River in Colorado. Wild was the correct term as it was completely uncivilized, with few towns and people, other than native Indians.
When beef from the great plains began to reach the east coast money became involved. The best cattle came from Texas. Men on horses herded cattle in droves up north almost 600 miles to towns in Kansas to meet the ever Westward moving railroads. These men were called cowboys. They were out on the trail for weeks and when they got to the rail-heads and received their pay, they were ready for almost anything. Mostly they were looking for fun and alcohol.
That is when wild behavior and wild women drove men drunk with alcohol caused a different kind of wild to apply to the area west of the Mississippi River. City Sheriffs and State Marshals did their best to contain them in what became called "the wild west".