It can be on either or both. I would suggest gathering on Christmas eve with distant relatives just in case of a storm or something you can reschedule to Christmas, or you can have one day for...
Could refer to spherical ornaments on trees ( rarely used by themselves- though I have seen holiday wreaths with balls attached, rather like a ferris wheel, or Balls in the sense of festive dances...
Christmas Eve is the day before Christmas (December 24). Boxing day is the day after Christmas (December 26), but can be later in some countries if Christmas Day falls on the weekend.