A register stores data, presented at its inputs, on the rising or falling edge of a clock input. A latch allows its internal data to be modified by data presented at its inputs until a latch control signal is asserted, at which time the latch's internal data is latched and remains unchanged regardless of the data presented at its inputs.
That would be my long answer, my short answer is: latches store data when a latch signal is raised, registers store data on clock signals.
Hope that helps
David