does charging up a laptop use about the same amount of energy as using a normal computer which is always connected?
charging laptop,, are you meaning charging the laptop batteries once the batteries are fully charged, energy flow to battery stops only energy required thereafter is for operating the laptop if you meant to compare operating energy of laptop v/s desktop, laptops are far more energy efficient just typically 40 watts for a laptop v/s 200 watts for a desktop
It depends on the battery and how much your laptop consumes power.