Persimmon – Kaki or Cachi, Loti – as they are known here in French/German and Italian.
We have seen two types of persimmon here all imported from Italy. By far the most lusciously sweet and soft fruit is the one on the right.  The one on the left is firmer and the texture resembles that of a mango, very delicious too but not as intensely sweet as the other.

When the fruit is ripe and upon handling, the very thin membranous skin ruptures.  The result is a gooey mess which requires a spoon to eat.
Look like tomatoes when they are packed ?

This time of year – November/December – is apparently the season for it.  Been buying it weekly. Yummy.

If interested, there is a wealth of information on this fruit on Wikipedia – persimmon.