A quick Google lookup shows that some plum varieties are called Prunes in English, and they don't need to be dried to be called that way.
> A prune is any of various plum cultivars, mostly Prunus domestica or European Plum, sold as fresh or dried fruit.
In the Wikipedia article about prunes you can see a photo of fruit looking strikingly similar to what you bought. Japanese Wikipedia and Goo Jisho indicate that in Japanese has the same meaning that it has in English
> (prune) (Prunus domestica)
This Japanese page gives further insight on the difference between plums and prunes.
I'm neither a biologist, nor a native English/Japanese speaker, but it seems most likely to me that the fruit you have bought are indeed called prunes in these two languages.
(I just copied my earlier comment by Nicolas' advice with minor edits.)