By definition, public land is land within the general public domain that a government holds in trust for its citizens. The government is the caretaker of public land. Public land is different than a public enclave (which actually IS owned by government).
Unfortunately, only by Wikipedia and Sierra Club definition. By law, the United States holds title to the land without any encumbrances or conditions of trust. This was originally done to facilitate disposal of the land by sale or grant which was the policy of the United States until 1976. In 1976, the Congress passed the Federal Land Policy and Management Act which changed that policy to retention and granted management powers to the BLM, NPS, and Forest Service to manage for “multi use”. The Sierra Club and others have invented the “held in trust” meme in order to leverage the FLPMA to kick ranchers, foresters, campsites, and marinas off of public lands.