For those curious about UI versions:
There are older versions, but didn't feel like digging them up.
This image shows Model S/X UI v6 (2014), v7 (2015), v8 (2016), v9 (2018), left to right.
View attachment 746867
Model 3 first production models ran v8 and very shortly after got v9.
v10 came out in late 2019. And we're about to get v11 any day now.
FSD beta version numbering was a bit cryptic at first. I believe the current versioning numbers started with v8 Dec 2020. Then in Jul 2021, v9 was released. The current version, v10 was released in Sept 2021, and the safety score generation of testers started getting access with 10.2 on Oct 11, 2021. As others have said, it's somewhat of a coincidence that the current UI version briefly matched the FSD version (10.2).
Firmware versioning just uses Tesla's internal build number. [YEAR].[WEEK#].[MAJOR].[MINOR]. Ex: 2021.36.8.10