As you mentioned, Japanese use '深層學習' instead of '深度學習' for 'deep learning'
(深層學習 is the preferred translation of 'Deep learning' in Hong Kong too)
Different countries and regions have different translations of some technological terms from foreign language. Hard to say which is better.
I didn't ask which is better or what meaning each word exactly has; I asked how it is determined and by who.
When a new terminology is coined in foreign language, different medias and publications may have trouble deciding on an unified translation.
Eventually, they will follow the lead of the authority in that particular field. If the Science journal in China translates 'Deep learning' as 深度学習, the news would adopt it and the general public will follow. Finally, dictionaries would make it official by listing it.