One is power, the other is energy. You are billed for the energy you use but the circuit ratings are in measurements of power.
kW is the power measurement
kWh is the energy measurement
A strong man could lift 200kg. This is his power. In order to do this he has consumed a bowl of cornflakes from where he got the energy (measured in kcalories which is another measure of energy like kWh).
1 kWh is constant power of 1kW consumed in 1 hour
It is also constant power of 2kW consumed in 0.5 hours
Or 10kW consumed in 0.1 hours (6 minutes)
So energy = power x time
1kWh = 1kW for 1 hour
If your house feed is 60Amp. Multiply this by 230volt you get 13800watt or 13.8kW. This is the maximum power you can draw from the grid before (eventually) your house fuse would rupture. But you could pull this power continuously. If you did this for 24 hours Octopus would charge you for 24x13.8 units = 331.2 units of energy (kWh) for that day.
This all applies to DC systems as well as AC systems. The main difference is that we transmit power around the country using AC as it allows us to transform the voltage up and down using transformers which helps us transfer large quantities of energy with reduced losses. For DC systems you need to use an inverter to convert between DC and AC. Batteries and Solar arrays can only work as DC systems so need to be converted (inverted) to connect to our grid systems. Many small household appliances eg computers and tv's convert AC to DC to work which they can do simply using diodes (after a transformer has been used to convert the voltage to a safe extra low voltage).
HTH