Not a huge difference. It is more about time. It's about to rain = it will rain soon/now. I'm about to sleep (fall asleep) = I will sleep soon/any minute/now. It will rain = some time in the future it will rain...maybe tomorrow. So, when I look at the clouds and think "it will rain any minute now!" I would say "It is about to rain. Let's go inside"....or in the South we would say "it is fixing to rain! Let's go inside".

نه داداش اولی معنی نزدیکه که بارون بیاد ولی دومی یعنی قطعا بارون میاد و بعدی میگی کم مونده خوابم ببره و دومی میگی خوابم میبره البته تا اونجایی که من میدونم