A laundry basket here is a wicker container for dirty clothes to be stored before they go in the machine:
Seems to be the general consensus on google images, too:
http://www.google.co.uk/search?q=lau...w=1024&bih=636
I have a plastic basket for clean laundry to be stored in before ironing and packing away, but when I think, 'laundry basket', my imediate thought is the type you have in your bedroom / bathroom to store dirty laundry and that's the way it is used here
Most people I know would not know the term "laundry hamper". Where I am from a hamper is commonly recognised as something you take a picnic in, or as per the topic of this thread, gift hampers.
But like you say, it's just a language thing - It really doesn't matter!
So, you know what I mean by hamper - does anybody else do them?