The first one has a key, which is supposed to symbolize Inari's role of an agriculture god and so it's fox servant has a key to the rice stores.
The second one is a jewel or ball which holds the fox's power or soul depending on the tale.
"Depictions of kitsune or people possessed by them may feature round white balls known as hoshi no tama (ほしのたま, star balls). Tales describe these as glowing with kitsunebi.Some stories identify them as magical jewels or pearls. When not in human form or possessing a human, a kitsune keeps the ball in its mouth or carries it on its tail. Jewels are a common symbol of Inari and representations of sacred Inari foxes without them are rare."
"One belief is that when a kitsune changes shape, its hoshi no tama holds a portion of its magical power. Another tradition is that the pearl represents the kitsune's soul; the kitsune will die if separated from it for too long. Those who obtain the ball may be able to extract a promise from the kitsune to help them in exchange for its return.For example, a 12th-century tale describes a man using a fox's hoshi no tama to secure a favor;"