There are those that think reality (including the universe) is just mathematics. Not modeled by mathematics, but is mathematics. To me, the mathematical universe hypothesis is starting to be the only theory that makes sense.
It might be a distinction without a difference, but I always understood the idea to be that objects we believe to be real are actually mathematical structures.
I see it as sharing some ideas from the we-are-living-in-a-simulation idea. If we were in a simulation, you wouldn’t say data structures and objects are real but would say the table in front of you is actually just data.
That's different from the world being mathematical or informational, which raises the question of what makes it real to us. What breathes life into the equations? Consciousness? Where does consciousness come into the picture?