They are the same item. Brolly is slang. Umbrella is the official name of the item. I would say that, in my experience, 'brolly' is very little said these days in Britain.

Brolly and Umbrella both are names of the same thing.Brolly is a slang word for Umbrella used in Britain, Australia, New Zealand and Kenya.

Same thing, just British versus American English. Brolly is British English.