British English:
To �wash up � is to wash the dishes, pots & pans after a meal.
To wash is to clean something with (soapy) water: wash the clothes, wash your face and hands, wash the car.
We wash down the walls of the house.
To cook / to do the cooking are almost the same, just slightly different usage:
She always does the cooking.
I �ll do the cooking tonight.
I �ll cook tonight.
She always cooks a cake for my birthday.
I want to cook some biscuits.
I �m going to buy my mother a gift.
I �m going to buy a gift for my mother.
I gave the gift to my mother.
