If the computer is simulating a spacetime, they're not the same.
You could - hypothetically - pause the computer, check its state, change a few variables, and the simulation would experience instant modifications.
A slow simulator could take many "real" time units to calculate each in-simulation time frame - and this would be invisible in-simulation.
And so on.
You have a fully causal system, but the simulation is ruled by its own independent emulation of causality.
Of course a computer implies a conscious user. But let's attempt some wild speculation and suggest that a "simulation" could also be a completely natural process - something that happens in a much bigger causal substrate: a kind of causal symmetry breaking, where a subset of possible relationships crystallises out of a bigger set of possibilities and then continues independently, losing some degrees of freedom.
A simple two level topology is the simplest possible model. But "causality physics" could allow all kinds of topologies - nested, circular, fractal, etc.
You could - hypothetically - pause the computer, check its state, change a few variables, and the simulation would experience instant modifications.
A slow simulator could take many "real" time units to calculate each in-simulation time frame - and this would be invisible in-simulation.
And so on.
You have a fully causal system, but the simulation is ruled by its own independent emulation of causality.
Of course a computer implies a conscious user. But let's attempt some wild speculation and suggest that a "simulation" could also be a completely natural process - something that happens in a much bigger causal substrate: a kind of causal symmetry breaking, where a subset of possible relationships crystallises out of a bigger set of possibilities and then continues independently, losing some degrees of freedom.
A simple two level topology is the simplest possible model. But "causality physics" could allow all kinds of topologies - nested, circular, fractal, etc.