It is all a matter of definition. They are both merely a physical structure, they both have to interact with very specific tissues in very specific ways to do anything, they both make our own matter replicate into additional copies of itself, they both have "preferred" areas of attack which are simply areas that they are more successful in, they both tend to "accidentally" cause behaviors that make us assist in spread (e.g. biting), and they both cause various bad things to happen as a side effect of their means of operation.

The prion's mode of operation isn't just "bump into stuff". It reaches the brain, causes other materials (DNA aptamers) to clump together, and causes other prions to be created.

That one happens to have a part that looks like genetic material and the other looks like a misfolded protein is merely a small implementation detail to me.

(Disclaimer: I, like everyone else I'm this thread, is not a qualified source of medical information.)