The natural world is the physical world, i.e. what you can see, touch, feel, smell & taste.
The supernatural world is the spiritual realm, and although we can't see it, it is just as real as the natural world.
Angels, Satan, demons, evil spirits, jinns, etc. exist in the spiritual realm.
We can 'reach the supernatural world' through spiritual things like prayer, worship, reading the Bible. God is invisible - He is in the supernatural world, the spiritual realm. But when He answers our prayers, we experience miracles in the natural world. Miracles are God's supernatural power at work in the natural, e.g. Jesus walking on the water. Naturally, no man can walk on water but supernaturally, yes. By the power of the supernatural God.
The occult also taps into the supernatural world, through seances, trances, ouija boards, crystal power, fortune-telling, tarot-card reading, transcendental meditation, worship of satan & evil angels, worship of idols, casting spells, & even magic....all of these occultic functions are through demonic powers. Evil spirits, demons, are spiritual beings & they operate in the unseen, spiritual realm. Witches, warlocks, magicians enlist the aid of these evil spirits to 'have power' over the natural world.