I would bet that the piano solo version would be exactly that, the solo part alone, without accompaniment.[...]
From my experience with concerto scores, I would tend to disagree with that. A piano solo arrangement is just that: the entire work written as a piano solo, with the solo piano playing the orchestral tutti
when the piano is not playing and with, at certain points the piano taking the melody when, in the original at that point, the piano has an accompanying role.
It wouldn't make much sense to have a "solo piano" version with only the solo piano part. What does the "solo pianist" do when the orchestra is playing and s/he isn't; sit there and count sixteen measures of silence?
A good case in point - since I don't have many scores of piano concertos that are "solo piano" versions, is the solo piano version of Gershwin's Rhapsody in Blue. The entire orchestral introduction is played by the "solo piano" which is not the case in the original version for piano and orchestra (jazz band).
Similarly, I have copies of both the "piano solo" version of Addinsell's "Warsaw Concerto" and there are several instances in the original with orchestra where the piano has an accompanying role against the orchestra's melody and, in the "piano solo" version the piano takes the orchestral melody.
I certainly wouldn't want to be studying a "piano solo" version to find out, eventually, that I'd not been playing the piano part of the piano with orchestra original.