Learn Spanish (Latin America): Aquella casa está allá.

While both mean 'that', they show different distances. You use esa for something that is somewhat close, usually near the person you are talking to. You use aquella for something that is far away from both of you, like a house way off in the distance.

What is the difference between allá and other words for 'there' like ahí?

These location words match the distance of the object you are pointing out. Ahí means 'there' (close to the listener) and pairs well with esa. Allá means 'way over there' (far from both speakers) and pairs perfectly with aquella.

Is aquella acting as an adjective or a pronoun here?

It acts as an adjective because it sits right next to the noun it describes, casa. If you dropped the noun and just said Aquella está allá (That one is over there), then it would be acting as a pronoun.

Why do we use está instead of es for a house? Isn't a house permanent?

Even though a house is permanently fixed to the ground, Spanish always uses the verb estar (here, está) to talk about the physical location of people, places, and things.