question about who's the son of who?

They're not blood related.

Can't stop the signal.

Initially Shun believed that Umi's father, Yūichirō, who was killed in an accident during the Korean War was also his father as Umi and he both had a photograph showing Yūichirō, Umi's adoptive father Akio and a third man. Umi had also checked the records and discovered that Yūichirō was entered as his real father.

Then it is revealed that Shun's father had actually been the third man in the photograph, called Tachibana, who was killed in an accident during the World War 2. His mother also died at childbirth and his other close relatives were killed in the atomic bombing. Umi's father Yūichirō had, out of kindness, registered Shun as his own son and adopted him, but soon decided to hand him over to Akio and his wife as they were better suited to take care of him.

There is also some doubt that Yūichirō could have been Shun's real father after all (as they bear a strong resemblance) and Shun and Umi could still have been half-siblings. Yūichirō might have had an illicit relationship with Tachibana's wife. However, captain Onodera (who knew Yūichirō, Tachibana and Akio) turns up and denies any such possibility, establishing that:

Tachibana and his wife were Shun's real parents.
Yūichirō and his wife are Umi's real parents, and Shun's initial adoptive parents.
Akio and his wife are Shun's current adoptive parents.
Umi and Shun are unrelated.

Thank you for this thread and for the clarification. I just saw the dubbed English version of the film yesterday and was very confused as to whom the young people were related to. I'm glad they were not related.