Elsa: But it's only for today
Anna: It's only for today
Elsa: It's agony to wait
Anna: It's agony to wait
Elsa: Tell the guards to open up the gate
Anna: The gate
Elsa is singing about wanting to hurry up, be queen and go back to trying to control her powers; her 'gates' is a metaphor for her introverting ways.
Anna, on the other hand, sings of her excitement to see real people for the first time since she was younger. When she was singing about the gates, she literally meant the gates; the doors separating her and the outside world.