Does this just mean there are less federal parks and more state and city owned parks?

Exactly. Until 1872, there was no precedent for the federal government setting aside land. The job fell to the states and local governments although it largely wasn't seen as the job of the government at all. In fact, before the Revolution, Thomas Jefferson privately purchased a natural bridge and the land surrounding it in Virginia for protection for posterity. The first action by the federal government to protect a large area of land was the Yosemite Grant in 1864, in which Congress ordered California to protect the Yosemite Valley and Mariposa Grove. With Yellowstone however, the area was still in Montana Territory. Following pressure from railroads to protect it (to entice travelers to a northern transcontinental route), Congress agreed to set it aside. There was no state government to give the park to though, and so Yellowstone was declared a National Park. By this time, most of the land out East had been either privatized or protected by the states. In fact, all National Parks east of the Mississippi are from donations to the Parks Service.