Hi, thanks for pointing this out! These are two different localization mechanisms.
Translations is the directory used by Captain of Industry’s built-in localization system and by mods that integrate with it directly. The lang directory is specific to MultiLangLib; the library loads these files itself from <Mod>/lang/<language>.json.
So the different folder name is intentional and not primarily related to the JSON structure. When using MultiLangLib, simply use the lang directory as described in the guide.
I hope this clears things up, and thank you for taking the time to read the guide!