Here's my observation and some thoughts:
1. Ups 'n Downs
5. A Moment's Notice
6. Caravan Riffs
11. Untitled
Sounds like studio recording, but w/ some (fake?) applause by a few people at the end of tunes(somebody yells "Bravo!" also) . Done by trio, with a non-distinctive bassist and a very shaky drummer. Bud doesn't play well, seems got juiced. "Ups 'n Downs" must be a Bud's original, but I'm pretty sure somebody else named it. The bassist takes solos in "Ups 'n Downs" and "A Moment's Notice"(yes, that Trane's tune) and uses pedal points heavily. Is this Scotty Holt? The drummer surely sounds like Rashied Ali when he plays straight four beat, conventional Jazz drums(AFAIK he is not really good at doing it even nowadays). "Caravan Riffs" is actually an alternate take of "Ups 'n Downs". "Untitled" is actually a Horace Silver's tune "No Smokin'". The drummer takes a very amateurish solo in them. I don't believe this "No Smokin'" comes from the Carnegie Hall Charlie Parker Memorial Concert(even if Bud played it).
3. Earl's Impro
4. Thelonious
8. Jazz Black/White
10. March To Paris
12. I'm Always Chasing Rainbows
Done by the same trio in the same studio (possibly at the same session), but without applause. Again most of tunes must be named by someone else, not Bud himself. "Earl's Impro" is similar to another Bud's composition "Monopoly". The bassist takes solo in it. "Jazz Black/White" is possibly based on "Almost Like Being In Love". On "March To Paris" the bassist takes intro solo. I don't think Track 12 comes from the Carnegie Hall concert, this is clearly a studio recording. Track 11 and 12 are bonus tracks, available only in MDCD 724.
2. Like Someone In Love
9. I Can't Believe That You're In Love With Me
Solo piano. Sounds like studio recording, without applause. But I won't be surprised if they come from Paudras' home recordings. Bud plays pretty well. "I Can't" is actually Bud's own "Buttercup".
7. 'Round Midnight
Solo piano. Bud plays pretty well. At the end it has a big applause in a big venue such as Carnegie Hall or Town Hall, but for me it sounds like a fake. I'm not sure this one is really from live recording.