Traditional Automated Guided Vehicles (AGVs) typically rely on predefined paths to complele sorting and delivery tasks, lacking flexibility. In recent years, the explosion of ecommerce, sustained growth in order volume, and the demand for flexible manufacturing with high-mix, low-volume production have posed new challenges to the logistics industry. Autonomous Mobile Robots (AMRs), with their capability for flexible route planning and intelligent environmental interaction, are gradually replacing AGVs as a focal point in smart logistics. This paper reviews the technological evolution from AGVs to AMRs, encompassing both intrinsic and extrinsic driving factors. By conparing performance differences in various scenarios, it proposes optimization solutions for key challenges such as path planning and multi-robot collaboration. In the future, further iterations of AMRs can be achieved through integration with 5G/6G, high-precision navigation, and human-robot interaction technologies.