What is the difference between 'do the washing up' and 'do the washing'?

Oh, dude, doing the washing up is like cleaning the dishes after a meal, you know, scrubbing those pots and pans. Doing the washing is more about laundry, throwing your dirty clothes in the machine and hoping you don't turn your whites pink. So, like, one involves soap suds and the other involves detergent, but hey, it's all just cleaning stuff, right?