Kaguya Houraisan is a princess and a person of Hourai who lives at Eientei. She used to be a Lunarian princess, but she was exiled to Earth for drinking the Hourai Elixir, which bestows immortality.
Fujiwara no Mokou is an immortal who lives somewhere within the Bamboo Forest of the Lost. She became unable to die after drinking the contents of a jar she stole from Kaguya―the Hourai Elixir.
Eternity is the same as being frozen in time. An eternal world is a world forever without history or change. On the other hand, an instant is an extremely brief moment in time, making it the opposite of eternity.
Kaguya and Mokou take advantage of their immortality to fight to the death each time they meet. If you visit the Bamboo Forest of the Lost, you might witness the interchange of Mokou's fire bullets and Kaguya's bullets of shining light, indicating that they are once again engaged in a fierce battle.
There is an old Japanese saying that basically means that fighting and arguing is a sign of friendship. This seems to apply to the relationship between Kaguya and Mokou. If you can seriously fight and argue with someone, you can show that person your true self. Friends like these should be cherished.