First, Shor's algorithm (as an example) cannot be expressed as a Universal Turing Machine. You are thinking much too small, software implementations on Turing Machines are possible for a strict subset of possible algorithms.

Second, even for algorithms which can be expressed as Turing Machines, you are giving the computer science equivalent of saying that a house and it's architecture drawing are the same. One is a thing which exists, one is a description of the thing. You cannot run an unimplemented algorithm without first doing the work of implementing it.