To answer your original question the verbs 'finir' and 'terminer' are synonyms and can be interchanged most of the time. Terminer is considered more literary so it maybe why it was the preferred option.
If you want to say you have finished something you will use either:
J'ai fini mon repas/j'ai terminé mon repas ( I have finished my meal)
If you want to say something has finished/ended, you will use 'finir' or 'se terminer'
Le film a fini à 10 h / Le film s'est terminé à 10h. ( The film finished at 10 o'clock)
Hope this helps!
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