"
good girl you always have to be
Conceal, don't feel, put on a show
Make one wrong move and everyone will know
Elsa: But it's only for today
Anna: It's
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.