China and India said they had negotiated a solution to a more than two-month-long standoff on a remote Himalayan plateau, ending a stalemate that had raised concerns about a potential military conflict.

But statements on Monday from both sides created confusion over terms of the detente. India’s Foreign Ministry said the two sides had agreed to the “expeditious disengagement of border personnel of India and China at the face-off site.” Beijing said Indian troops had withdrawn and, responding to a question about Chinese troop...