The linux installer is listed as two files, but when I download them they both have the same name and each appears to be a full installer by itself.

I installed both versions. The game installed from the part two installer works without issue. The game from the part one installer needed a file to be marked as executable, but then it also ran fine.

Comparing the two installations, the game files are identical, but some of the mojosetup files are different
$ diff -qrN Terraria Terraria_alt/
Files Terraria/.mojosetup/gog_com-Terraria_1.desktop and Terraria_alt/.mojosetup/gog_com-Terraria_1.desktop differ
Files Terraria/.mojosetup/manifest/Terraria.lua and Terraria_alt/.mojosetup/manifest/Terraria.lua differ
Files Terraria/.mojosetup/manifest/Terraria.xml and Terraria_alt/.mojosetup/manifest/Terraria.xml differ
Files Terraria/.mojosetup/meta/gtk-2.0/pixmaps/background.png and Terraria_alt/.mojosetup/meta/gtk-2.0/pixmaps/background.png differ
Files Terraria/.mojosetup/scripts/config.lua and Terraria_alt/.mojosetup/scripts/config.lua differ
Files Terraria/start.sh and Terraria_alt/start.sh differ

Some of the differences are just because of the install path. But there are a bunch of changes in the manifest xml and lua files. I didn't check but it might just be the order of the contents are different because the files are almost the same size.
There is also a minor difference in the start script
diff -r Terraria/start.sh Terraria_alt/start.sh
19c19
< chmod +x *
---
> chmod +x "Terraria"

So it looks like part two is the correct installer?

I used the two installers consecutively, and game works fine. Later I tried using only the first installer, and the game doesn't launch. Then I ran the second installer, and the game was functional again.

EDIT: now 18/05/2020 we have 1.4.0.2 installer, yay! I have yet to try multiplayer, but version should be same on steam too.

I just downloaded the linux version.
Now there were only one file but it has nearly the double size ( 529 MB) of the Windows installer (271MB)

After installing the game (Linux Mint 19.3) the game won't run.
I have looked into start.sh and found the line:

chmod +x "Terraria"

After I changed this line into:

chmod +x *

the game starts.

But there were no option to change the resolution of the game. I play usually in 2560x1600.
Terrible.

To get Terraria 1.4 to launch on Linux, you can simply delete the line:

chmod +x "Terraria"

in start.sh and the game will still launch.

everything worked perfectly for me when I tried the gog installer.

But I notice that there is no 1.4.0.2 hot fix update so that is a thing.