As they are written, they mean the same thing. However, if you add a specific time-frame to your hypothetical, then you should use "is raining". For example, "If it is raining when we wake up next Saturday, we will stay home." or "If it is snowing when we arrive, we'll have a snowball fight."

they have the same meaning. both are correct.

If it rains next sunday we will stay home and watch tv. Is correct. Using it's is wrong here. It's is used as a short form for "it is .. Now as you can see there is no need to write "is"in this sentence. Also, no need to write Sunday in capital.