Both your sentences refer to the same real-world event, so in that way they are the same. What changes is your attitude to that real-world event.
It will storm tomorrow is essentially a statement of fact. You are giving information. I find it helps to think of this as looking at the 'outside' of the event.
It will be storming tomorrow is concerned with the sequence of events between the beginning and the end of the storm - this is looking at the 'inside' of the event.
Change the event to 'going to work on Sunday'...
Speaking to your boss, you would probably say "I will work on Sunday". All he wants is the information, that fact that you will be there.
Speaking to your friends, who want to know if you can join them for a game of cricket, you would probably say "I will be working on Sunday", because the sequence of events between starting work and finishing work mean that you have no time to play cricket.
Same event; different aspect.