Correct usage of "will be" vs. "will"

This is a question about the difference between expressing the future by using will + the plain form of the verb, and expressing it by using will + be + the -ing form of the verb (the progressive form). To show the difference, it’s first necessary to adjust the examples a little:

As it will be raining all day tomorrow, we need to go shopping tonight.

As it will rain all day tomorrow, we need to go shopping tonight.

The first is much more likely to be what a native speaker would say. It emphasises the continuous nature of the rain suggested by the adverbial all day. In fact, in this context the second version with will would hardly ever be used. If the weather forecast is for rain, but not necessarily for prolonged rain, a speaker might say As it’s going to rain tomorrow . . .

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.