What is the difference between the two?

Postal 2 Complete Original Version is basically the old, original version that was released in December 2003 as "Postal 2 - Share the Pain" (which included new difficulty settings, new levels, a multiplayer mode and two minor instances of censorship compared to the original retail version from April 2003) back in 2003 plus the Apocalypse Weekend expansion.

The Offline Backup Game Installer is the latest, up-to-date version which includes lots of new content, most of it taken from the "A Week in Paradise"-mod (new weapons, Apocalypse Weekend-style dismemberment for the entire game, ability to play all the whole week in one go, additional voice overs, one instance of censorship from "Share the Pain" getting reinstated and much, much more). Since the two versions are drastically different, the Complete Original Version was retained as an extra for nostalgic value (play Postal 2 the way you remember it).

Lemme try and explain this better.

Offline Backup Installer = MOST RECENT/CURRENT VERSION
This version is the most uptodate version that has the most content. sadly tho the gog version of it does not include any signs of support for mods and/or MP. This version also supports the new Paradise Lost DLC

Postal 2 Complete original version in Extras = Old v1409 Before the 1409X patch
This is the version from gog youll want if you want to enjoy any MP from the game. This version also supports mods. This version sadly tho does not support the new Paradise Lost DLC

That should answer the need to know questions ya may have.

I don't know if mods would work (never tested any) but working MP is included with the most recent/current version. Just got into the "ShareThePain\system" folder and launch the "Postal2MP.exe". It works fine.

After some patches, and maybe after Paradise Lost DLC installed - Share The Pain included with current version can't host the game. And I don't know how to fix it.

But, Postal 2 Complete Version - have worked Shared the Pain.

I think some files with new content broke the MP, because MP version is still 1409, as title screen sayd.