I have got my sticky paws on my Birthday Discount, though I had to ask Customer Care for it. I got a CC40-prefixed one, which seems to be a special ‘Customer Care 40% off’ one. I think it’s single use, but it does seem to work with all the Exclusions (at least in my basket, I’ve not used it yet 
). And it’s valid for 30 days. 
I don’t know if the actual emailed out birthday one is different (standard or unlimited), but maybe someone else got a proper one and can chuck in some comparisons?