The flat space holography program aims at describing quantum gravity in asymptotically flat spacetime in terms of a dual lower-dimensional field theory. Two different roads to construct flat space holography have emerged. The first consists of a 4d bulk / 3d boundary duality, called Carrollian holography, where 4d gravity is suggested to be dual to a 3d Carrollian CFT living on the null boundary of the spacetime. The second is a 4d bulk / 2d boundary duality, called celestial holography, where 4d gravity is dual to a 2d CFT living on the celestial sphere. I will argue that these two seemingly contradictory proposals are actually related. The Carrollian operators will be mapped to the celestial operators using an appropriate integral transform. The Ward identities of the sourced Carrollian CFT, encoding the gravitational flux-balance laws, will be shown to reproduce those of the 2d celestial CFT, encoding the bulk soft theorems.