In same order of list you referenced with compatibility information. Additional information about packages used to build each version is available but will not be supplied by me unless requested, you can get a good idea about that info by visiting the distrowatch puppy linux page
Scroll to lower section of page for base packages
https://distrowatch.com/table.php?distribution=puppy
Compatibility refers to the Linux version all the core packages originated from.
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Compatibility * Architecture Latest Version
Ubuntu Focal 64 x86_64 64-bit FossaPup64 9.5 - Latest official 64-bit Puppy Linux Ubuntu Focal Fossa compatible
Raspbian Buster armhf 32-bit Raspup 8.2.1 - Raspberry Pi version of Puppy Linux
Ubuntu Bionic x86 32-bit BionicPup32 8.0 - Latest official 32-bit Puppy Linux Ubuntu Bionic Beaver compatible
Ubuntu Bionic 64 x86_64 64-bit BionicPup64 8.0 - Older official Bionic 64-bit Puppy Linux Ubuntu Bionic Beaver compatible (this was 64-bit version released before latest Ubuntu Focal Fossa version)
Ubuntu Xenial x86 32-bit XenialPup 7.5 - Older official 32-bit Puppy Linux Ubuntu Xenial Xerus compatible (this was 32-bit version released before latest Ubuntu Bionic Beaver version)
Ubuntu Xenial 64 x86_64 64-bit XenialPup64 7.5 - Older official 64-bit Puppy Linux Ubuntu Xenial Xerus compatible (this was the 64-bit version released before the Ubuntu Bionic Beaver version)
Slackware 14.2 x86 32-bit Slacko Puppy 7.0 - Latest official 32-bit Slackware based Puppy Linux
Slackware64 14.2 x86_64 64-bit Slacko64 Puppy 7.0 - Latest official 64-bit Slackware based Puppy Linux
Slackware 14.1 x86 32-bit Slacko Puppy 6.3.2 - Older official 32-bit Slackware based Puppy Linux
Slackware64 14.1 x86_64 64-bit Slacko64 Puppy 6.3.2 - Older official 32-bit Slackware based Puppy Linux
Ubuntu Trusty x86 32-bit Tahrpup 6.0.5 - Older official 32-bit Puppy Linux Ubuntu Trusty Tahr compatible (this was 32-bit version released before the Ubuntu Xenial Xerus version)
Ubuntu Trusty 64 x86_64 64-bit Tahrpup64 6.0.5 - Older official 64-bit Puppy Linux Ubuntu Trusty Tahr compatible (this was 64-bit version released before the Ubuntu Xenial Xerus version)
These are all tried and true,
32-bit computers will need a 32-bit version.
64-bit computers can use either 32-bit or 64-bit versions.