In addition to installing and launching the games, there are cloud saves, achievements, time tracking, leaderboards for achievements (which integrates Steam achievements for anyone who's linked their Steam profile), overlay, some multiplayer stuff, and more. In this respect it has social features and game management features similar to what Steam has.

GOG Galaxy is also meant to be a universal launcher so you can use "integrations" to have Galaxy launch other games through their respective clients and even have it close the client afterwards. You can also add your own independently-installed games, as long as they show up in a database of games that they use (I dunno where it's from but these days it has pretty much everything I've looked for, aside from romhacks, but for that matter, I'm pretty sure you could make it launch any executable with any label and Galaxy wouldn't question you). That said, I'm used to just launching things from game executables directly so I don't use it for this anyway lol.

Also Galaxy offers more flexibility with managing game installs than the Steam client does. For one, you can set the install directory to anywhere, rather than being locked in Steam\steamapps\common\gamename. And pretty importantly IMO, there's an easily accessible (though non-default, which is fine IMO) option to tell the game to not update, and the Galaxy client won't try to force you to update (unlike the Steam client). (EDIT: there's also a universal default for whether to auto-update games, in addition to per-game settings.) On top of this Galaxy also has more UI options than Steam does, e.g. having a List View option (which Steam unceremoniously junked several years ago in favor of their current mess).

I'm actually about to check out its ability to download standalone installers. I started a couple very big game downloads last night on my browser and they failed so I'm gonna see if the client can do better with stuff like resuming downloads.