Generally, it is the same meaning for 'older sister' but two different ways to say it as other teachers mentioned.
However, traditionally, 언니 can be used for 'older siblings in the matter of same sex'.
For example, a girl can call her older sister 언니 and a boy can call his older brother 언니 too. (but not for different sex)
It is like, a married woman calling her older sister-in-law as 형님. (형 generally mean 'older brother' but it can be interchangeably used with 언니)
In conclusion, 누나 = for a boy to call his older sister. 언니 = (1. for a girl to call her older sister, 2. for a boy/girl to call older same-sex siblings)
형/형님 = (1. for a boy to call his older brother, 2. for a married woman to call her older sister-in-law).
Hope this explains more.