Haemoglobin present in Root Nodules of Leguminous plants is called Leghaemoglobin.
Both are involved in gas exchange, though the main function in plants, which is the delivery of oxygen and CO2 transport, probably does not play much of a role. The reason is that leghemoglobin is necessary to deliver oxygen to symbiotic bacteria. However, the bacteria are there to fix nitrogen and they can only do it at low oxygen concentrations. So the leghemoglobin has a very strong binding constant (higher than hemoglobin) in order to ensure an extremely low amount of free oxygen, but still ensure delivery to the bacteria.
While in Humans the main function of hemoglobin is to Delivery of O2 and CO2 transport from the cells to the lungs where it is removed from the body.
Other than that the functional groups are essentially the same, but the overall protein structure is different (both on the sequence and somewhat on the structure level). Both belong to the same protein family, though.