Is the phrase "ほしのこえ" ("hoshi no koe" / "voice of star") used in a Japanese proverb or something similarly common? I've noticed that it's the title of two things that I enjoy: the movie by Makoto Shinkai ("Voices of a Distant Star") and the album by Nobukazu Takemura. The two don't seem related, so I guess it must be some commonish Japanese phrase.

just a coincidence, I'd say. Sort of like when 2 songs have the same title.

How do you tell it in different languades if you use direct translation.
Translation like "voice of star" is really exact but how did they find this whole phrase "Voices of a Distant Star" is such a short think like "ほしのこえ".
I'm not good in english and I know little of japanese but i can say that word "distant" is not used in japanese part?
"Hlas hviezdy" is translation to my language (slovak).

Poetic license