The greatest commonality is UIKit. tvOS and iOS share core APIs, architecture, and philosophy on how to put apps together and structure them for event handling and view-by-view presentation.
The greatest difference is interaction.
iOS hosts the most immersive interaction style currently possible, where you physically touch the interface and manipulate it with a custom language of gestures. The latest generation of iOS devices takes this even further, adding additional nuance through 3D touch. Its motion system further turns the device into the experience, integrating its orientation and movement into the real world.
tvOS in term creates the greatest barriers between the user and the app basically possible. No keyboard (and no, devices don’t count), no fixed mapping between touch and screen, and essentially a button and a limited motion system for input.
With iOS, you sit next to your screen. With tvOS, you sit across the room.