After updating to BIOS 1.21 (Dell XPS 15 9570 System BIOS | Driver Details | Dell US), Device Manger is reporting a version of 1.20.
However, both Dell Update and System Information (msinfo) are reporting 1.21 (I still need to reboot again back into BIOS to confirm what it reports, just haven't had the opportunity to yet).
In this case I would only trust what the BIOS displays after you boot into the BIOS (F2).
I've see this before with my own laptop.
the version in device manager will only change once the new firmware is offered and downloaded from windows update. no update actually takes place if you've previously manually installed the latest version but somehow this windows update corrects what you see in device manager.
I actually did in fact manually install it b/c the dell drivers download page had the newer version available despite neither Support Assist, Dell Update, nor Windows Update detecting it.
I have seen Windows Update queue up and "install" drivers, firmware, even the BIOS, that was the same version already installed. I know these can be blocked, but sometimes are too quick to catch. During such an update the install progress bar flickers to 100%, and even though the update shows as installing successfully in history, I think what really happens is a passive acknowledgement that the same version already existed, and is skipped (maybe it is through this mechanism that the Windows version numbers become consistent, as you were mentioning, otherwise I wouldn't see a point in the update being detected in the first place). I suppose to confirm this I could always check the modified date of the driver files.
By the way, you are sure that is a BIOS version listed in Device manager?
Device manager usually doesn't list BIOS version.
In your first post, second image, select Firmware, what are the details ?
First off, this is not a problem! All it means is Windows has not pushed the current Bios to the computer. Give it time and it will do exactly that. You can try to force it from the Driver tab > Update Driver > Search Automatically .., but if the update is not available it will say the best driver is already installed