"Appetite" can refer abstractly to any form of craving, not just for food.
Medieval philosophers and theologians often discuss the bodily appetites.
"I am an appetite." —Nosferatu
It can refer specifically to a person's (healthy or unhealthy) desire for nourishment., their wanting to eat food each day:
The child had a poor appetite and was losing weight.
Now that the worst of the flu had passed, her appetite was returning.
Constant snacking on junk food is often a response to boredom or anxiety, not a sign of a healthy appetite.
That meaning can be used figuratively:
She had lost her appetite for romantic comedies.
"Hunger" refers literally to aacute or chronic craving for food :
She ate some granola to stave off hunger on the hike.
He had never known true hunger until he was shipwrecked on a small island.
but is used figuratively for any sort of craving:
The man seems to have an insatiable hunger for gold.