2 minature pieces my Grandmother gave me as a child from Japan

by Ann
(Nashville, TN)

Hello,
I have 2 small pieces my grandmother gave me as a child. They have much sentimental value to me, but I have always wondered what they are and what the stamps on the bottom say. My grandfather was a career Army officer and they lived in Japan for a few years. My father says that his mother purchased many pieces from families there due to the hard times of the period. If anyone can help me with any information, I would be very grateful. Thank you in advance for any comment or insight!

The small blue vase is 3 inches tall
The rust box is 2 1/2 by 2 1/2 inches