Umbrella-ella-ella

Ok. I hated the song. But where does the word 'umbrella' come from? Well `umbra' is latin for shadow so umbrella presumably means something that creates a little shadow. But then what is the difference between `parasol' and `umbrella'? Well 'para' on the front of anything seems to mean `almost but a bit less' (paramedic, paramilitary, parambulator, paracompact(!)...) so `parasol' ought to mean something like `less sun'. Technically, then there is perhaps no difference between the two. Maybe the French have got it right with 'parapluie' which I guess means `less rain'...