I don't think they are saying anything similar at all. Julian Barbour finds a way to get rid of Time completely (by saying every possible state exists and there

I don't think they are saying anything similar at all. Julian Barbour finds a way to get rid of Time completely (by saying every possible state exists and there must be some law that favours states that _seem_ to be related to _apparently_ previous states). Wolfram is more focused on making sense of 'time is change' through the lens of computation.