Malbim: The fire, and the wind that lifted him, hint that he was stripped of physicality. The only elements [of the four] that remained in him were fire and wind, which are light, and could lift him. As long as the body is composed of the four elements, the soul can separate from the body only via death. However, after the fire singed the two heavy elements (earth and water), like the fire singed the earth and water on Har ha'Karmel (Melachim I, 18:38), the separation was between Eliyahu's soul and body. His body became like a garment that one can wear or remove, as he wants. Then he ascended to Shamayim. Just like in the Supreme chariot, stormy wind and fire flashing [amidst a cloud] surround Nogah (radiant light), so before he ascended to Nogah they surrounded him. The great cloud already departed from him, for he already split the water when he was in the Yarden.

Radak: Regarding physicality, ha'Shamayim is the air of the sky (Ta'uf ba'Shamayim" - Devarim 4:17). Regarding Ru'ach, it is the higher Shamayim with the angels - "Halelu Es Hashem Min ha'Shamayim" (Tehilim 148:1). Eliyahu became [totally] spiritual and his body was consumed in the Supreme fire. Every element returned to its place.