Why does GOG say Version 1.02, but Steam says Version 1.03?

Are they identical or is the GOG release based on an older version?

Not all the time, but many times, the GOG version of a game gets updated behind Steam. It's simple numbers. Devs, especially small ones, first devote their resources to the largest number of users first. Since most of GOG staff are off on the weekends, even if the devs send over an update today (as an example), it won't likely get updated till Monday or Tuesday.

Usually the wait is not very long between Steam and GOG on updates.

The offline installer file name is:

setup_relicta_1.02_(64bit)_(41842).exe

(plus several -N.bin files). Good to hear it is the latest. It didn't work for me, but I'll start another thread for that (edit: turned out to just be really misleading error messages when running out of disk space during the install pocess). Thanks for showing up in the GOG forums :). You can also let GOG know about your account (if you haven't) and they will give you special yellow text.