Think of max demand relating typically to multiple final circuits fed from one distribution board, such as a domestic installation or a sub main feeding part of a larger industrial installation. Where not all final circuits are drawing full power simultaneously. Although some individual final circuits do have their own diversity due to the load connected, such as a cooker that is not using all rings, grills and ovens simultaneously. Whereas the design current and full load currents relate to your calculations used when selecting cables for a single final circuit with a specific known, fixed load, or assumed load, socket outlets, to be connected.
For example a domestic installation may have a 9kW shower a 3kW immersion heater and cooker circuit that has 12kW worth of elements but typically only 8kW is running at one time. Although the three circuits could potentially be 24kW if all added together. The maximum demand may still only be 9kW as the user is not cooking whilst in the shower and the immersion only comes on a night during economy 7 rates. The individual circuits must have cables suitable for connected loads design currents but the distribution board and incoming tails only need to be large enough to cater for the maximum demand after diversity applied not the sum of all the design currents.
Doc H.