They are countable, but yes there are many ways, but that alone doesn't mean it's capable of meaningfully evolving. It's a search space multiple orders of magnitude smaller than a piece of DNA, so it's easy to see how a different successfully propagating misfold will be significantly less likely when starting from an existing propagating misfold.
If you are suggesting one propagating misfolded protein can, by chance, misfold into another propagating misfolded protein at a rate fast enough to become adaptive... then it's qualitatively the same as a virus, but I don't see this as likely given the significantly smaller search space.
The space of possible proteins - and thus prions - is not at all limited, neither figuratively nor literally. It is most certainly not "countable" without some Nobel-prize inducing discovery.
The only known human prion proteins seem to be a few orders of magnitude smaller than that though, and they don't appear to adapt.
Are you saying it's possible for prions to emerge from large proteins with the ability to adapt?
That a virus can be a big and complicated structure does not mean that smaller and simpler structure is fundamentally different.
Viruses themselves also have many different modes of operation, with things like virophages, satellite virus and giant virus showing just how unclear the term "virus" is.