Console ports enable console connections using, usually, a USB to db9 connector. These ports are usually used when first setting up a switch were the technician has physical access to the switch.
Management ports are usually normal rj45 female ports that can be connected with any cat cable, this port type has IP functionality and can run ip services such as SSH to provide remote connectivity to manage the switch. On layer 2 switches this port is the only one that provides layer 3 functionality.