There's no difference, as a Mexican I can say both expressions and have the same meaning.
Do you cook? yes! I do, I enjoy/like cooking my own food.
or "haciendo" like you said...
oh!, smell delicious, What did you cook? I've cooked mole, but this is a lot of work! yes, but I'm enjoying cooking mole because it reminds me my beloved grandmother.
hey, it's Sunday, come on! we should go to the cinema, today is the premier.... yes, I would like to go but I must do the laundry and cook lunch. Then, let me help you.. really? yes, well ok, but I'll choose cook, you know I love/enjoy cooking more than home chores!! Do you agree...?
I'm an English student too. I hope I've been able to help you.