A prion can't arbitrary replicate from "food" or "host", its replication is more like a damaged version of protein X that can damage that same protein X if it encounters it. In many aspects it stays the same protein - the exact same DNA, the exact same sequence, just folded differently.
A virus can overtake a cell and mobilize its resources to create a bajillion copies of that virus. A prion can transform only as much copies of that protein as that cell has made in its normal processes.
A bacteria replicates at a much smaller rate than a virus.
A virus requires a cell to replicate, bacteria require a much more limited range of hospitable environments.
Both bacteria and viruses "attempt" to create exact copies, just as a prion does. Admittedly prion replication probably has more accuracy, but that prions occur at all indicates the process allows for natural selection.
These don't seem to put prions outside of the "replication" category - they replicate by encountering other proteins, so they are in a body. Their rate of replication is limited (or boosted) by the rate of encountering these proteins. They attempt to create copies of themselves with the chance of failure or different end result.
A virus can overtake a cell and mobilize its resources to create a bajillion copies of that virus. A prion can transform only as much copies of that protein as that cell has made in its normal processes.