Thanks for your question, Erich.
I am not necessarily familiar with flower/tree names but I know there are five kinds of cherries in my old temple - Shitennoji Temple.
They are -
Somei Yoshino(Prunus yedoensis)
Shidare Zakura(Weeping cherry)
Yae Zakura(Double-flowered cherry tree)
Yamazakura(Cherry)
Hachisukazakura
I've found many cherry trees with whitish flowers there.
As 70% of the cherries in Japan is said Somei Yoshino, I think they are it as you pointed out.
Following photos show others.
The first one is remarkably Shidare Zakura(Weeping cherry).
The second looks a little differently from Somei Yoshino but probably still Somei Yoshino.
The third one would be Yamazakura(Cherry) as it looks wild species.
The last one is, I guess, Yae Zakura(Double-flowered cherry tree).
I don't know where the Hachisukazakura is.