Both sites are selling fakes.
There is a genuine factory outlet shop at Bicester Village - the prices there are what you will pay for a previous season bag. Mulberry (and most other luxury brands) do not sell "seconds" they do sometimes sell "samples" but these usually happen at industry sales and are made up of items that made it to production but not to the collection.
Some fakes are extremely good copies and many people would struggle to tell the difference between a real and good fake, especially when the fake is new (they don't tend to wear as well as originals, so easier to spot on an older bag)
Dust bags, boxes, receipts and "care cards" are all red herrings and come as standard with a "decent fake". I could get you a mulberry that comes with all those things and looks almost identical here in the Middle East without too much bother at all.
And that is my public service announcement over for the day 